Actually I believe the note at the bottom of the table covers this. So #2 would work with no adjustments but with NM you need to adjust by using the 60C column
Using the 60C column is not an adjustment. An adjustment is for number of CCCs per 310.15(C). A correction is for ambient temperature per 310.15(B).
But the restriction on Table 310.12 to the case of no correction factors does mean for outdoor conductors that you can only use it in geographical locations where the ambient temperature does not exceed 30C = 86F. [For warmer locations, you probably won't need to upsize from Table 310.12, but you need to do the computation based on temperature correction of the 90C ampacity to confirm that, rather that just read the Table.] Of course, if you are considering NM, that means it is not running outdoors at all, but it could be running indoors in an unconditioned space or other location that could exceed 86F (*). In that case the letter of 310.12 precludes the use of #2 NM for a 125A dwelling unit feeder.
Even if the NM is only run in locations that will be at 86F or cooler, the spirit of 310.12 precludes the use of Table 310.12 with NM.
Cheers, Wayne
(*) For a perhaps persnickety example, let's say you are running NM in an insulated exterior wall. The interior will be conditioned space not to exceed 75F, while you're in a climate where the proper exterior temperature to use is say 97F. 86F is half way between 75F and 97F; does that mean that to avoid needing to apply temperature correction factors, you must ensure that the NM is within the interior half of the thickness of the insulation, where the temperature is expected to be 86F and under, avoiding the exterior half of the thickness of the insulation, where the temperature may exceed 86F?