Is the Unit obligated to update the PT card that a SPC (P) took before going to BLC or should the most recent PT card from BLC be updated?

Looks like you already discovered this but NCO academies are now required to update all PT and HT/WT stats in DTMS. It is one of TRADOCs ways to increase academic rigor, and frankly because many of the units are not sending their folks to school-prepared which this requirement also holds them accountable.

The most recent score is the current score.
Entering a previous score does not help for points.
Also, an APFT prior to BLC might have been a diagnostic for school, not record, and therefore not necessary in DTMS and certainly not points for promotion, and would be the reason why your unit would not enter it in DTMS, or they did enter it as a diagnostic, which is why you don't see the points.

What you should be looking into at your unit is grading standards for the APFT; if a Soldier scores 280 at your unit then only scores a 210 a short time later at BLC, then it's likely you have graders at your unit that do not understand the standard for pushups and situps, and/or your 2mi run route is too short.

How do you go from a 280 to a 210???? That is his fault for staying physically conditioned. He did that to himself. Unless say he was in an accident or got injured in that time gap.