First, my personal evidence is anecdotal. I was suffering greatly from depression and suicidal thoughts. Other religions provided zero relief. I tried some of the Buddha's suggestions for the specific ailments. They worked, to my astonishment and delight. The Buddha became like a good friend who helped me through a very bad time. On those grounds, I trust his other teachings to be true, even if they're not relevant to my current situation or beyond my understanding.
The opposite, too btw - in the Sutras the realisation of emptiness is always declared as something to rejoice and be happy about but funnily almost all people on this planet find exactly that things are empty rather displeasing and do a great deal of work to forget about it.
I'm not so sure people are spontaneously having an experience of emptiness and then finding it displeasing and trying to put it out of their minds. I say this for a few reasons.
One, to realize emptiness requires a great deal of deliberate practice, because emptiness isn't normally available to us through our widespread habits of agitation and confusion. Tell me what color that wall is, but just ignore the disco lights, laser show, and fog machine
Second, even if a person has a naturally calm and unperturbed mind, slapping a label "unpleasant" on emptiness means it's no longer emptiness: it's an unpleasant interpretation of emptiness, basically the same thing as unpleasantness.
And third, from what I've read and heard, an experience of emptiness is possibly like becoming aware in a dream that everything is a dream. It feels solid enough, but every perception and experience you have is made of the same, insubstantial stuff: the dream. Experientially, phenomena become even more vivid and bright in their lack of substance. It sounds quite remarkable, and liberating.
It's not the same thing as the dreary, meaningless, nihilistic, "life is empty, sigh" that perhaps some people may feel sometimes.
If thats right or wrong of course is another matter and maybe seeing ourselves even on a biological level in the way that we are would have the potential to take negative aspects out of our societies.
I think it's important also to stress that from what I understand at least, Buddhism isn't about favoring this concept over that. One reason I found the Dharma so compelling was that, unlike many religions, it stresses the inseparability of good/evil, light/dark, certainty/uncertainty. The constant tension of one trying to triumph over the other is largely absent in Buddhism, and a cause of great strife in the world.
In fact, there are practices that specifically instruct to embrace the negative mental formations we normally run away from (e.g. tonglen). One of the points is to show the sheer relativity of any concept, that when you stay with your anger or sadness and look at it closely, it's made of the same insubstantial mist as everything else. A lot of the time, it even loses its visceral impact. How many people are compelled to increase suffering around them on account of mist? And yet, this gives rise to great compassion because we've all been there, tormented by shadows and the tales we tell ourselves.
I'm not suggesting Buddhism condones negativity. The accumulation of merit, positive deeds/thoughts/etc., is a crucial part of practice because it tends to lead to circumstances with less confusion and distraction, which otherwise complicate practice. A master could meditate through a toothache. The rest of us need a little help. So by no means is there a rejection of the negative aspects, things about us we wish we didn't have. Cut off the right side of something and you have a new right side. We need our neuroses and people who drive us nuts to motivate us to practice, and to provide opportunities to perfect the paramitas. Otherwise we'd all be sipping nectar in the god realm, totally blissed out and unconcerned with our own confusion.
Samsara/nirvana are similarly two extremes, and relative/absolute as well. They're gateways from our normal mode of operation in extremes to a third option: both and neither; not one, not two.
I hope I'm not making this too complicated. The actual gist is so simple it's stupid. Here is one of my favorite quotes on the matter:
the outer world and all its inhabitants,
are appearances of our own mind.
Appearances are mind,
appearing and yet empty,
empty and yet appearing.
Appearances are inseparable from emptiness,
deceptive like a dream or an illusion.
They are nothing and yet they appear,
like the moon on water.
To recognize this
completely liberates us
from our deep entanglement
in dualistic grasping and fixation.
Free of artificiality, relaxed and loose,
open to that freshness
that is the very nature
of self-aware consciousness.
Aside from this,
there is nothing to contemplate or meditate on.
don’t do anything.
Simply remain undistracted.
I beg you -
meditate naturally and let go!"
- Gendun Rinpoche