It's not likely, but that doesn't mean that it's not possible. Bluetooth uses Frequency Hopping Spread Spectrum technology which means that the signal is split among the (supposed to be) clearest group of available channels. If there is a lot of radio noise (other headsets, WiFi, or anything else that emits RF waves in the same frequency range) interference can still be possible.
But that would more likely cause static rather than force the headset to disconnect.
My bet goes to the bum device.