“Who” is not giving you the time off per the regs? It’s not the “company”, it’s an individual acting in name of the company who’s got his own interpretations.
So who is it? The Chief pilot? The DO?
Are they the same person?
If you’re 135 you have a FAA POI.
See if you can get the other pilot to play ball with you, if not go at it alone.
Arm yourself with some documentation and interpretations and go see whomever it is, CP or DO.
Don’t know what state you’re in but record the meeting on your phone.
Ask your CP or DO for an interpretation from the POI. If he refuses then offer to get one yourself.
Don’t threaten (yet) but insist that you would greatly appreciate your POI’s input in this.

Here’s my personal opinion without looking anything up:
This is a common 135 scam.
POI will do a paperwork inspection ( which is always looking back) and see all legal rest.
But they should look forward too, they rarely do.


If this argument gets out of hand and you get fired then get an aviation attorney to contact the FAA to whistleblow on your behalf.
You’ll have a TMAAT story to tell at your airline interview: yes I’ve been fired because I refused to participate in illegal and unsafe practices.
With only two pilots your employer is in a very weak position to threaten.