Even then, I'm wondering if it not might be better to simply specify that if an FP-based PRNG is passed, then the closing conditions "[0 .. 1)" or "[0 .. 1]" are simply the passed PRNG's ("[min .. max)" or "[min .. max]", or even (min .. max] or (min .. max)).

Honestly, I think It's the best we can actually guarantee. I a PRNG never produces min, then you aren't actually producing "[".

Besides, all the FP-PRNGs I know of are "[)" anyways (I know it's not a strong argument, but one none the less...).