I'm not sure with that statement, in my experience users have enjoyed having live support, if it's used correctly.Most users don't bother if you have 24/7 support online. They want their requests to be resolved in a timely manner. Though, we do provider unmanaged vps etc. but we do provide support to managed service question except when the support requests are at peak.
That would be a misclasification and false advertising. It's no different to saying you have 24/7 phone support when all you have is an answering machine.however the former can be classified as 24/7 even if staff are only checking it during business hours.