Quote
15 amp circuit trips when heater plugged into it. Nothing else on circuit.
Ammeter reads 12.5 amps at breaker.

What is wrong with this picture?

A circuit-breaker is set to trip at 1.5 (150%) times the stated label current, this is what most of us call I2t (the square of the current multiplied by time)
(Higher current, shorter time)
All non-adjustable circuit breakers are the same, provided they are of the appropriate "curve ratio".

Now, IMO, this breaker should not be tripping until it senses at least 22.5A, on the thermal side of the breaker (as opposed to the magnetic side, that senses gross overloads, which should trip instantly).
I suspect a bad breaker.