Major game companies such as Type-MOON rarely, if ever, pull a stunt like "SURPRISE, DUAL RELEASE".
There is nothing that suggests that such a "dual release" is even a credible or appealing option to Type-MOON on any level. You can list the advantages of a co-op project that "keeps the fans in the dark", but as long as those are not in TM's view they are moot points.
It is in their best interests that fans know what's going on, rather than keep the fans in the dark for no good reason.
We know that this isn't actually happening but it is possible to do something like this.
(Protip: Defeating your whole argument with the final line of said argument is a bad idea)
Also, I don't understand why you would bring up the "possibility of dual release" as a counter-argument when your entire emphasis was on "facts and proof"; especially since "possibility of Tsukihime 2 not existing" is infinitely greater than the "possibility of dual release"
The fact that there have been no such news of co-op or Tsukihime 2 is sufficient to prove that it is a joke, even if you didn't get that from the screenshots ("Blue, blue glass moon, under the cerulean air").
Once again, no news whatsoever of Tsukihime 2 serves as proof that it does not exist. As for interviews or whatever, I guess the closest it gets is Nasu saying at some point they're working on something new (although this was more directed at Fate rather than anything else).
If you're unwilling to accept that and would much rather bet your money on a "theory" (not even that, as theories require proof via experimentation. All you're offering is a hypothesis) then there's really not much to say.
Sorry if this comes off as aggressive or anything.