Exactly right! Too often we see those mate-in-1 problems "solved" by e.p. first moves that are invalid.
A new blog I wrote covers the subject: Chess problem conventions re castling and capturing en passant. It gives a very economical example of a mate-in-2 problem with a valid e.p. key-move, and the blog finishes with an advanced mate-in-3 example that's mind-bending.
Here's a different one, a mate-in-3 that's easier. It's a twin problem, i.e. there's a different solution when the WK starts on e8 instead.
Every once in a while, someone posts something to effect of the very hard, if not "world's hardest" Mate-in-1 Puzzle.
While you need to adhere to all the rules of chess, there is one specific rule (in international chess composition) regarding using "En Passant":
1. En Passant can only be used to achieve mate if it can be proven that last move black played was moving a pawn forward two spaces.
I suppose there are problems out there with more than a single move that also starts with an en passant move, as long as it can be proven that black's last move was a double pawn move.
As a side note: under the established rules of chess composition, white always moves first. At least in modern days. Not sure when that rule was adopted though, or if it's been like that since at least the 1800's, which I'll use as a cutoff for modern chess compositions. -That is, I'll say problems composed before 1800 will be considered pre-modern, for this thread anyway.