Alright everyone, I think I might have an idea of WHY this bug happens!
It occurred to me while I was practicing a bit with Sektor. Instant air teleport is one of his most important tools, but sometimes I wouldn't jump at all when performing it. So I tested it further and figured out that if you tap Up then immediately return to neutral, your character will not jump! This makes instant air specials extremely annoying to pull off BTW, particularly Scorpion's (which is very hard to begin with) and Kabal's.
So I looked into this and while I can't say I have conclusive results or anything, my brief testing strongly indicates that the input bug occurs when you tap a direction then let go within a few frames. So if you're Scorpion and you want to beat a close jump-in with Down+1, and you press Down~1 then instantly let go of Down after 1, there's a chance you're going to get a standing 1 and eat a jump-in combo.
Personally, this helps explain why as Kano I would sometimes get a standing 4 when attempting to beat wakeup moves with d+4 xx knife - I was probably canceling the d+4 too quickly.
tl;dr - It appears that this game does not read directions (at least Up and Down) at all until they are held for a certain amount of time, and that's at the heart of the problem here. For now, you'll have to hold Down for dear life when attempting your crouching AAs and such.
As for how to fix this, the first thing I would say is that we as a community need to test this more to make sure this theory is correct! If this post turns out to be right, I would personally recommend just having the game read directional inputs ASAP. I have a feeling they did this to make moves ending in Up easier, but you could increase jump startup a little bit if that's the issue. That's been Capcom's standard solution...notice how Zangief has the slowest jump startup in most SF games.
If there are other reasons then please enlighten us - this is the biggest problem left in this game!