The instrument you seem to be referring to isn't an altimeter but a barometer, and altimeter reads height/altitude based on a reference pressure which is set by the user, it doesn't tell you the pressure although it can be roughly shown by using the altimeter in reverse as such and adjusting the reference pressure until the altimeter shows 0.
Aside from that (and if I understand your question correctly), the higher Hg then the higher the pressure as you said yourself, so your colleague who would think that 29.98 is higher pressure than 30.22 is wrong. However, if you genuinely did mean an altimeter and not a barometer, then if the reference pressure is not changed and the altimeter decreases (for example if you adjusted the reference so the altimeter reads 500' and over the course of an hour it decreases to 400') then that does mean that the pressure is increasing.