CV boots don't hold fluid in the transmission. That's held in by a seal in the transmission housing. That they told you this is all you need to know about AAMCO.
Get your car out of that ripoff known as AAMCO, and into a small local shop - ~~they'll source a good used transmission and replace it,~~ likely for half or less of what AAMCO is going to charge you. Edit because I missed you already found one.
I replaced a Honda transmission recently (auto), it was $800 via ebay (came from an outfit that sells large components like this). It arrived perfectly clean, wrapped and pallete. Then replaced it in an afternoon.
If the TCM was bad, it would've died before the trans quit... So you would've had lights, and it wouldn't have shifted. The transmission dying isn't going to kill a TCM. Losing fluid means the clutches overheat and glaze, which really reduces their coefficient of friction (they slip). Nothing about that would affect a TCM which is a very robust, purpose-built, control module (some would say computer, I'd say more like a CNC). Sounds more like they hooked it up wrong, or the wrong transmission was sent (sometimes there are similar transmission thatcan look nearly identical, but have different configurations of controls).
AAMCO is a combination of incompetence and snake oil salesmen.