Simon Finch's answer gives the parallel case. The series case is exemplified by the common-base amplifier:
simulate this circuit – Schematic created using CircuitLab
Note that Vin = Vbb - Vbe, and Vbe varies with Ic. Meanwhile, output is relative to input, that is, Vce. And we can reasonably assume (i.e. for Vce > Vce(sat)) the currents are approximately equal. So the output voltage contains a fraction of the input voltage, and thus power as well.
Granted, it's a tenuous argument, especially for small signals. But if we measure all the way up to clipping, we'll clearly see that the output voltage peak can be slightly higher than Vcc.
For the BJT, it's a very small fraction added, anyway; which is to say, the transconductance and amplification factor are both very high. For devices having less, the fraction can be much higher. Vacuum tube triodes especially can have an input (cathode) AC voltage as much as, say, a third of the output.
These two methods (common-base, and follower, bootstrap or parallel-adding) are not at all exclusive; a real circuit can have a linear combination of both, thus giving a mix of both characters, as well as neither (a common-emitter or other topology). They could also be inverted, which seems rather counterproductive, but often input or output power is simply burned wholesale as a means of improving bandwidth, stability or distortion.
To really know what's going on, you'd have to measure the power inputs and output quite accurately. Only additive methods can have seemingly anomalously high efficiency (where a fraction of the input really is adding to the output). Such an amplifier could have apparent efficiency (i.e. taking DC input versus AC output) higher than the theoretical class B maximum, of course on closer inspection it's merely the case that the added power obeys that limit.
Of course, any type can be made to have arbitrarily poor efficiency, so having some figure is not exactly proof of anything!
If I had to guess, my guess would be your amplifier in question uses a combination of attenuation and feedback to ensure stability for ease-of-use, at expense to efficiency. In that case, the topology really doesn't matter. Common-emitter (or source) would be most likely, as most devices are available packaged that way (i.e. with the source/emitter hard grounded to the heatsink tab). But an inspection of the internals, or a review of the service manual, would say for sure.