In your base sentence, There is no way, the noun way is what determines what constructions may follow. Way takes (as we used to put it—today the technical term is licenses) the following constructions with the sense [Subject] can prove X
- a way to prove X
- a way of proving X
- a way for Subject to prove X
- a way (that/in which) Subject can prove X
- a way (that/in which) X can be proven
This is true whether your base sentence is There is no way or There is a way or There may be a way or There are many ways or any other variation on this theme: way determines what constructions are permissible.
But when you drop no way you change the entire structure of the sentence. The construction There is, by itself, can only take a noun phrase as its complement. None of these constructions will work.
The apparent counter-examples you cite belong to different structures:
To someone infected by the conspiracy theory virus it doesn't matter how much evidence there is to prove that 9/11 was indeed an attack ... Once you unpack the relative clause, the relevant piece of the sentence boils down to There is evidence to prove that X.
There is less evidence to support the supposition that Foster's death was a homicide than there is to prove that Nicole Brown Simpson was ... Again, after unpacking, the relevant piece of the sentence boils down to There is more evidence to prove that X.
Evidence performs the same role in both of these as way in your sentence, governing what constructions are permissible.