I've seen both sides of the spectrum. It doesn't take much research to find out how much manpower is behind a network infrastructure. There are hosts that have only a few customers that can get away with working part time and there are hosts that truly are a fully managed, round the clock, hosting company. It's the small one man shops that pose as hosting giants that get into trouble in the long run.
All other things equal, it comes down to the work load and how large their operation is. Because so much of our business can be outsourced (for lack of a better word) such as support, server and data center maintenance, etc. it isn't difficult for someone to run a business with a half a dozen decent sized customers and do well part time. This approach isn't exactly inferior to a complete in-house fully managed IT solution. It's strictly a matter of customer satisfaction and honesty between you and your customers.
So is Hosting a full time job every time? I guess the answer is "It depends..."