psrr simply means that internal to the chip the crosstalk between the supply and the output
every 20db is another power of 10, so 120-6, (larger gains suffer more crosstalk) comes close to 1/500,000th of the supply noise
so your 1V of noise would be 2uV of noise at the output, now i would like to remind you that when uV's matter to you you really need to rethink designs, as even a massive thick ground plane is going to shift by more than that over a balanced star ground any current flowing through any trace will need to be planned out and such, even leakages between traces begin to matter,
to take it a little bit furthur, for a normal linear supply your noise is generally around 10mV, so 20nV effective noise on the output, and just about everything else in the circuit would far outway this, even parasitic capacitance variences over temperature begin to matter at that level,
so for what type of sensor would be effected by it, it comes down to what your doing, i would imagine accurate voltage or current measurements, or voltage references and current references,
as for why the lab power supplies may well be near that 1mV of noise, using a pass element cripples that psrr, so short of using one heck of an op amp to supply 3-4A your op amp has to correct for every small fluctuation on the pass elements input, equally to get a fast response of the output voltage and the ability to current limit generally requires a fairly small output capacitance,
on top of all that pass elements have capacitances, turn on delays and turn off delays, which limits how fast the loop can respond to the noise,