NEC explicitly requires that when different voltages are present in a facility, that different receptacle configurations be used.
But it does not specify _which_ different configurations.
NEMA does associate configuration with voltage, but the NEMA configurations are a design choice, not code.
IMHO using standard configurations is a 'best practice'.
If a facility has 480V receptacles, but chooses to use what are typically 600V devices, than that is fine. But if there is both 480V and 600V present, using the 600V configuration for both is a violation.
Using 6-20 devices for both 208V and 240V in a single facility is also a violation.
In the OP's situation, if 6-20 devices are used for both 240V and 277V, then there is a code violation.
If the actual devices used have a 'maximum working voltage' rating < 277V, then there is a violation.
Imagine a facility with both 208/120V and 480/277V. Pretty common. But the facility as built color coded the 208V with black, purple, orange, and 480V with red, yellow, blue. Would you demand that the re-wire?
-Jon