You're referring to implication then, i.e. P => Q <=> !P || Q and in that case, I definitely agree. ;-) That's also why I started my comment with a propositional "if" on how one could define "no meetings" and "no communication" to show that there is something to be said for the P != Q interpretation.
In short, I believe neilk should have used => instead of !=. Or just plain english. ;-)
"Meetings != communication" is analogous to saying "At meetings, communication doesn't necessarily occur."
In terms you would personally appreciate: (No Patrick Hernandez != No Dancing) similarly is not equivalent to (Patrick Hernandez != Dancing)
One says without Patrick Hernandez, there may be dancing. The other says with Patrick Hernandez there certainly is not any dancing ;-)