>I have no problem with pure mathematics, my training was in it; but it seems very possible to me that most people funding theoretical computer science (as opposed to pure maths) probably assume the work has a more realistic computational model backing it up.

Most people getting funding for pure maths probably just lie and/or stretch the truth that it tangentially has some relation to or possible benefit to practical things like cryptography. It doesn't need to actually be true. It just needs to feel true enough.