The odds are against it being anything other than water in the tank.
Having two exhaust valves fold simulaneously and then also have neither one of them unfold itself during the dive is extremely unlikely. An identical failure in both second stages is a very, very low probability occurence anyway, which leads up the chain to a possible first stage problem.
But...any hole, leak or damage to the first stage that would let large amounts of water in would not happen as the same problem would first let large amounts of air out - and flooding would not be an issue until you were out of gas anyway, so that indicates it was clearly not a first stage problem. When first stages fail it is almost always in the form of passing excess gas past a damaged seat or orifice. In exceedingly rare cases where a mainspring may break, a first stage could possibly fail closed and deliver no gas at all. Everything else that is possible just results in fairly minor amounts of gas leaking past a bad o-ring.
That leaves the tank. And a situation where both regs deliver water when you are in a head down position is a classic example of having either an awful lot of water in the tank or, a still impressive amount of water in a tank with a missing dip tube (which normally keeps a small to moderate amount of water from finding it's way into the reg.)
Tear down of the reg in this situation should show signs of flooding and possibly contamination from corrosion products, salt, etc that may have been in the water. The filter would usually show evidence of this on an external examination.
If it happended to me, my first act on surfacing and getting back aboard would be to disconnect the tank, invert it and crack the valve to see what happens. If you find your self holding an impressive imitation of a super soaker, you've found the problem. Finding (or proving) that same problem is much harder after your annonymous rental tank finds it's way back into the rental tank rack.
If water in a rental tank caused the problem, the shop needs to cover the cost of the teardown, drying and annual service of your reg (and I'd do a full annual service as bits of rust, corroded aluminum, salt, etc, do bad things to o-rings and seats and they should be replaced.