There are few hard semantic rules in English; it is more a matter of conventional usage and expectations - and when 'all' is used, people usually expect that the sentence is about at least one thing, and probably more. I suspect that this is mainly a matter of omission: in ordinary discourse, there seem to be few occasions for using it when it is definitely the case that the resulting sentence is not referring to anything (or exactly one thing), and if there is doubt about the existence of any referents at all, an alternative phrasing along the lines of 'if there are any X, then...' would be considered the right way to say it.
This is so much so that if you use the 'vacuous all', people will suspect that you have ulterior motives, and are being deliberately obtuse to hide them.
I wonder whether, if we attempted to make explicit all these tacit rules and conventions, we would end up with a consistent logic, and I believe that this looseness of natural languages was the main motivation for formalizing logic, from the enlightenment onward.
given that this is a liar the use of all may be meant to deceive, the main thing here is the use of the word conclude.
I doubt, given in what context this was written, that this is a matter of omission.
I agree in general but I do wonder how unusual using ‘all’ to assume existence is. For example “have you done all your homework?” What we are really asking is whether there is any homework that wasn’t done, not did you do any homework.