Can someone explain, why the third party did not multiply the current by 1.25 on 2B. Is this also correct?
The third party is correct on the 1.25 factor. The 1.25 factor for continuous loads is only for terminations, not for the wire itself. The ampacity of a wire is already a continuous rating, per the definition.
This is reflected in the NEC in the various sections discussing this. For feeders, 215.2(A)(1)(a) is the termination check and includes the 125% factor for continuous loads (and does not include derating, although that is only expressed by the wording contrast with 215.2(A)(1)(b)). While 215.2(A)(1)(b) is the wire check and does not include a 125% factor for continuous loads.
Note that the third party selection is still wrong if the continuous load is on a 300A non-100% rated breaker, as reflected by your "this forum" line. This is due to the interaction of 240.4 and 215.3 (or comparable section if this is not a feeder).
To summarize:
Termination check:, no derating, use 125% factor for continuous portion of load, use ampacity column based on termination temperature rating
Wire check: derate, use ampacity column based on insulation temperature, check ampacity against both the load (no 125%) and the minimum for the breaker size selected. If a major portion of the load is continuous, the breaker size check is likely to control this check.
Cheers, Wayne