I haven't seen any major host advertise 24/7 support and then not provide the same after hours. It could be and apparently is true from the comments and personal experiences posted above, but only for companies that are operating on a much smaller scale and don't have the manpower or resources to man their helpdesks at night.

You can't run a web hosting company without it. Servers can go down at any time and other problems can arise without notice. Someone should always be on duty monitoring servers and answering support tickets at all times, otherwise you'll get negative reviews and claims of false advertising which is bad for business. Billing and sales queries can be delayed by a few hours because they're not as critical as support issues, but most companies prefer to handle sales as rapidly as they can because of the competition that exists in this industry.