As some of the more recent posts suggest, the GA may have given the OP the correct overall "bottom line".
We just don't know without more facts, including the a/c seating size and whether weight and balance issues were involved (although the OP's observation about giving the seat to another suggests that there may not have been a wt./balance issue). However, whether or not the OP was entitled to be compensated as an IDB, if the GA did not first seek volunteers, the DOT would likely consider this an IDB situation for statistical reporting and for enforcement purposes, even if OP was not entitled to IDB compensation.
There are indeed cases where the IDB compensation is far less than the typical VDB offer. One easy, mainline example: an A320 is oversold by 3 but all three are protected on the next flight scheduled to arrive at the ticketed destination 0:58 minutes after the oversold flight. IDB compensation will be zero; VDB comp. will be whatever offer is made and accepted by the pax. (i.e., $200 voucher). (See 14 C.F.R. sec. 250.6 (d).)