It's even worse than that. Not "the response is based ... " into which it might be possible to read something comprehensible; but "the 'possibility' of a response, is entirely dependent ... " That is, it is not being stated that if the little green men of the planet Tharg send a message, then how that message appears to you is based on your assumptions (which your prime number example is designed to refute).
What is being stated is that the possibility that you will perceive any received message at all is entirely dependent on your assumptions; ie that whether or not the little green men exist, and are able and inclined to communicate with you, are not in any way factors in the probability of you receiving a message.
All observations require an observer (a mind).
Until someone can come up with a test which demonstrates that an observation can be made entirely independently of a mind, that's just the way it is .. like it or not.
It all
starts with how our minds relate to our perceptions. That's just what minds do. Our perceptions are intrinsically linked with our senses and our minds. There's heaps of objective evidence for what I'm saying.
There's no objective evidence that 'something exists' independently from our minds. Its just a
belief that it does, (due to the
lack of the above-mentioned objective test).
Science treats this belief with neutrality .. the same as it does for the belief in the existence of some supreme being .. no different (until, that is, you can come up with that test ...
then we
might have something to talk about ... and we'll be using our minds to do that, too).
Oh, and
nothing I've said is solipsistic .. if you think it is, you need to look up what that means, and
observe that what I'm saying, is
not consistent with that definition.
PS: I'm gong to go back to talking about Proxima b and the scope for what can be
observed. If you wish to continue the above diversion, then I suggest you create your own thread on it.