Basically, the school is obliged to do what is in THEIR procedure under section 504.
They have to follow their own written guidelines.
MANY schools find it simpler to simply write up "we'll follow items 1 through 10 on our IDEA compliance safeguards" rather than have two separate standards-- but legally, they CAN make the ADA compliance (under 504) different. If they want to.
What that means is that you should be asking for procedural safeguards in writing, and for any procedural protocol that they follow-- you know, so that you "understand the process better."
(If you're looking for a way to know without coming off as highly adversarial, I mean-- and I strongly encourage you to be polite at the outset on this score.)
As for not needing parents involved, well... that depends. Technically, no, they don't HAVE to do so... but in the case of children with medical reasons for possible eligibility, it opens the school up to a world of hurt if they haven't "considered" a wide variety of sources of expert input. If they've EXCLUDED one expert input stream (and really, it's pretty hard to argue that the primary manager of a child's FA day to day for many years is not "expert" in that sense) then they just opened themselves up during due process if you wound up there.