The perfect-and-sudden [method of practicing cessation-and-contemplation] involves taking the true aspects [of reality] as the object from the very beginning. Whatever is made to be the object [of contemplation], it is the Middle; there is nothing that is not truly real. [When one attains the state of contemplation wherein] reality itself (dharmadhatu) is fixed as the object [of contemplation], and thoughts are integrated with reality itself,[then one realizes that] there is not a single color or scent that is not the Middle Way. It is the same for the realm of the individual, the realm of Buddhas, and the world at large. All [phenomena experienced through] the aggregates (skandha) and senses (ayatana) are thusness; therefore there is no [substantial] suffering that needs to be removed. Since ignorance (avidya) and the exhausting dust [of passionate afflictions (kleša)] are indivisible with bodhi-wisdom, there is no origin [of suffering; i.e., craving] to be severed. Since the extreme [dualities] and false [views] are [indivisible with] the Middle and what is right, there is no path to be cultivated. Since [this cyclic world of] samsara is [indivisible with] nirvana, there is no extinguishing [of craving] to be realized. Since suffering and its causes do not exist [substantially], there is no mundane world [to be transcended]; since the path and the extinction [of craving] do not exist [substantially], there is no transcendent world [to be gained]. There is purely the single true aspect [of reality-as-it-is]; there are no separate things outside this true aspect. For things in themselves (dharmata) to be quiescent is called “cessation”; to be quiescent yet ever luminous is called “contemplation.” Though earlier and later [stages] are spoken of, they are neither two nor separate. This is called perfect-and-sudden cessation-and-contemplation.
Mohezhikuan (Moho Chih-kuan), Tr. Swanson
That's probably the most famous passage from the Mohezhikuan by Zhiyi. I highlighted one phrase - "thoughts are integrated with reality itself". That, IMO, points to the insight that informs the teaching on the Buddhanature of Trees and Rocks.
One of the hallmark analytical devices in Tiantai is the radical application of mutuality. This is a passage that is quoted in Ziporyn's Evil and/as/or Good that I think illustrates it well:
In Vasubandhu's theory of consciousness-only, there is only the one consciousness, but it is divided into the discriminating and the undiscriminating forms of consciousness; the discriminating consciousness is what we usually call consciousness, whereas the undiscriminating consciousness is "consciousness appearing to be an object" (sì chén shí / 似塵識). All the physical objects in the universe- vases, clothing, carts, and carriages- are all this undiscriminating form of consciousness.... But since they are all one nature, we can equally say that there are two forms of matter, the discriminating and the undiscriminating.... It is in this sense that the mind and matter are non-dual. Since he [Ven Vasubandhu] is able to say there are these two different forms of consciousness, we can equally say that they are two different forms of matter.... In the Integrated Teaching we can also say that all things are matter only, or sound only, or scent only, or flavour only, or tactile sensation only, or consciousness only. In sum, every dharma inherently mutually possesses all the dharmāḥ comprising dharmadhātu.
Swanson and Ziporyn use different terminology, but "Perfect" and "Integrated" refer to the same thing.
What Zhiyi seems to be pointing out is that for Vasubandhu, the dharmadhatu, the phenomenal world, is a function of the Mind, and the various dharmas are actually mere aspects of the Mind. We project dharmas. Some of these projections are simply mistaken. Some of these dharmas are pure perceptions. Zhiyi does not disturb that. He goes a step further. In the Perfect/Integrated teaching, mutuality is complete (Integrated/Perfect), such that the Mind is also understood to be a function of the Dharmadhatu as well as the various discrete dharmas. Ziporyn summarizes this as Omnicentric Holism - any dharma, true or false, is the complete Dharmadhatu. Pick any dharma, and one will find that the Dharmadhatu is integrated completely.
Mind and matter are not dual, but rather mutually continuous. When we think that Mind is different than matter, its because we have a particular idea of Mind and Matter. Zhiyi is pointing out that there is a level of insight where that distinction loses meaning. Mind is matter, matter is mind. The Green Cup is a function of my mind. My mind is function of the Green Cup.
This is of course the "positive" way to discuss it. The negation is another way to discuss mind and matter, "Neither Mind nor Matter" - its a different analysis with different insights about the nature of reality. We're here dealing with the positive.
By mutual is meant that one is not before the other. (Zhiyi says they are not "vertical"). They are also infinite in their multiplicity and yet mutually arisen and so indistinguishably integrated ie. one (Zhiyi says they are not "horizontal").
When we say that Rocks share Buddhanature with Sentient Beings, this is a statement about the nature of reality, not Buddhanature as the sort of simplified idea of the literal Buddha Seed (tathagatagarbha). The sentient being itself is recast at this level of insight as a particular vantage point on reality rather than a discrete being (I use the term "nexus" to describe it, as it can be applied equally to sentient and insentient beings). The idea of a sentient being privileges the nexus defined by the 5 aggregates as a discrete thing (horizontal distinction), and that serves as the lens through which reality is understood (vertical hierarchy). When these are flattened out, the sentient being become redefined in the context of the whole, as the whole. And this applies to every phenomena.
The contemplation of this is the Mohezhikuan. The Great Cessation and Illumination.
There are a few sutra passages that are referred to in connection with this teaching.
Chapter 1 of the Vimalakirti Sutra, the Buddha addressing Sariputra
“Śāriputra, it is through the transgressions of sentient beings that they do not see the purity of the Tathāgata’s (i.e., my) buddha land. This is not the Tathāgata’s fault! Śāriputra, this land of mine is pure, but you do not see it.”
And from the Lotus Sutra, the Buddha addressing Maitreya:
When sentient beings see themselves
Amidst a conflagration
At the end of a kalpa,
It is in fact my tranquil land,
Always full of devas and humans.
Because of the mutuality of all dharmas, all nexii are intrinsically Buddha. The reason is that the Eternal Buddha is fact and is integrated in the Dharmadhatu. When Buddha is taken as the Middle, all dharmas, all beings, being completely integrated, are Buddha. Similarly, when a hell being is taken as the Middle, all dharmas, all beings, being completely integrated, are Hell.
Rocks have Buddhanature because they are integrated with Buddha. Rocks also have hell nature because they are integrated with beings suffering in hell.
That's my stab at it. Probably wrong.