There are a few circumstances.
1) power is removed from the system for an extended period of time. this should be the state the emulator presents. what initial states can happen after an extended absence of power? The game that doesn't boot in FCEUX and does on real hardware seems to prove that FCEUX initial state is NOT a valid one by those standards. it's initial state should be one that is likely to happen on a real console.
2) power is left off for a very small amount of time. this causes a minor change in state from what it was when it was powered off. on my c-64, for example this tends to cause one bit in each ram cell to flip on. the same one. this cannot be accurately emulated, so it seems this is NOT valid.
3) power is never actually dropped because person holds reset button while removing cart 1 and inserting cart two. this is possible on real hardware. so it's a valid TASing trick, in my opinion. you dn't even ave to press reset until after swapping the game. a real life example here
https://www.youtube.com/watch?v=wyiBuX9y16k
the movie attempted a variation of number 3.
according to nesdev people, uninitialized ram after long term poweroff is mostly FF, with some memory locations having a single bit at 0. this confirms my experience with c-64 that a quick power off and on flips one of the bits to 1. So seems FCEUX is wrong, and that Nestopia is more correct.
However, someone changing games reasonably quickly can produce a very different result (not an uncommon event in real life).
So seems "random" initial state should randomly select values from the following pool
FF
FE
FD
FB
F7
EF
DF
BF
7F
with an extra high priority given to
FF
if it's to reproduce real world conditions from long term poweroff.