I'm not "relying" on it. It's just a fact.
I know you are. I think this is where you -- and others -- are getting lost.
What "action type" -- under the D&D rules -- is the attack allowed for by a casting of snake's swiftness? Is it free, immediate, swift, move, standard, or full?
What "action type" is an AoO? Is it free, immediate, swift, move, standard, or full?
(The answer to both of those is "none of them.")
These are not "actions" -- in the rules sense -- at all. They are actions -- in the English language sense -- that may or may not provoke AoOs of their own, however.