There are other options.
One is that he did not take less than he was worth, and that he got what NFL teams see his value as. After all, the entire NFL could have made him an offer, and he took the deal he did.
Another is, assuming for a minute he did take less than he was worth, perhaps he just preferred Denver over other NFL teams. Otherwise, why would he take less than he was worth?
Another is we offered something competitive with Denver, but Denver’s offer was slightly more.
Something some fans seem to lose sight of is that the Cowboys don't somehow have first dibs, or a right of first refusal, on every free agent. If a free agent doesn’t sign with Dallas it doesn’t necessarily mean Dallas either showed no interest or made a lowball offer. There are 31 other teams the Cowboys are competing with.