Bluetooth does use compression to get higher quality sound out of the relatively low bandwidth (vs what a wire carrying an analog signal can handle, which is continuous in both time and amplitude domains, so effectively infinite sample rate and bit depth, though it's limited by what the DAC can put out as well as what the recording ADC (and/or mixing software) picked up in the first place).

There's a set of codecs in the Bluetooth standard and devices don't have to support every codec in that list (iirc some are proprietary and need to be licensed, plus more support requires more circuitry or firmware if it's decoded by a programmable decoder). I'm guessing that's what they are talking about but asked in case they did mean they thought not seeing mp3 and flac on the list meant they can't listen to songs encoded in those format.

Edit: closed a bracket