That's obviously true. However, this all started with the statement (variants of which hjave been repeated) ...
If "for a given power output" does not mean "for a given [i.e. a particular] power output", then what on earth does it mean?
However, I confess that I'm getting rather confused, presumably due to my ignorance of how motors work', when looking at the figures in the catalogues he's been posting (figures which I need to study and play with more carefully).
If power output (hence also power input, if we assume that efficiency remains unchanged) remains unchanged, then if an increase in supply voltage results in current remaining unchanged or falling, then the only possible explanation is that PF has reduced. That does happen (in the figures in the catalogue), but it doesn't look (on 'eyeballing') as if PF falls by anything like enough to explain the behaviour of current (I need to do some sums to check - by that's the impression of my eyeballs).
If, as seems to be inevitable, the (somewhat non-intuitive) behaviour of current is the consequence of a reduction in PF, by what mechanism does the PF reduce when voltage is increased? As you say, the increased voltage will result in a very small increase in speed, but that looks (in catalogue figures) as if it's only a tiny increase in speed (generally no more than 0.2%, other than for the smallest motors, when it can be as high as ~2%) nowhere near enough to 'cancel', let alone 'reverse', the effect of increasing voltage by about 9% (from 380V to 415V).
As said, I'm going to play a bit with the numbers, since my first impression from eyeballing the figures doesn't seem to 'add up'.
Kind Regards, John