As cerebropetrologist said above, impressment only applied to British subjects. The fact that some British subjects also held paperwork (with varying degrees of validity) describing them as US citizens did not relieve them of their duty to the crown.
There were undoubtedly various cases in which unambiguously American citizens who had never taken an oath of allegiance to the British crown nor had been born in the Kingdom of Great Britain or United Kingdom were pressed into service as was documented by the meeting of family members with impressed children before and during the War of 1812 (without even raising the issue of whether it was possible to forfeit one's citizenship in the era). And the investigation process was very flawed; the sailor in question was assumed British until unambiguously proven otherwise, was not given any exemption from duty (and thus was punished with what any reasonable human would describe as torture if they refused to execute their duty) or aid in pursuing their case, and could not draw pay without forfeiting their right to appeal their impressment; even if they refused to draw pay and chose to appeal their duties were not modified and they faced flogging at best if they refused to carry them out. I'm pretty sure that being forced to work on threat to life and limb for an extended period of time is slavery by any reasonable standard, though it wouldn't have been chattel slavery (i.e. slavery where the slave is treated as property similar to livestock) but something more similar to serfdom on the German (as opposed to Russian) model. And there were certainly US sailors in the British Merchant Marine and Royal Navy (both volunteers and who had given allegiance in some form to the UK and thus were legitimately impressed), a number of whom even fought at Trafalgar. The Davis situation is rather ambiguous, as he was taken into service on a US soil (i.e. the US did not violate the sovereignty of the British flag); I find it possible that, considering that the USN was an all-volunteer service at the time (Lavery, 1989), Davis enlisted whilst inebriated (possibly having been deliberatly made drunk before being goaded into service by an officer or inkeep) and thus technically not impressed at all, though he certainly did not consent to serve by a modern standard. Many other British sailors did serve in the USN enticed by better pay and conditions; the issue of the legality of impressment here lies not in whether it would constitute slavery or forced labor in removing the sailors (as they were British subjects) but rather what right the Royal Navy had to halt and board a naval ship of a sovereign, neutral nation on the high seas. In no case did the American government deliberately and formally authorize impressment, whereas Parliament undoubtedly had. Might a US officer have impressed British subjects at some point? Possibly. But the United States, unlike Great Britain, never made it an instrument of policy to coerce citizens of other states into service (which was undoubtedly true as even when the appeals process existed it was certainly biased against the sailor in question).