Fortunately, this is happening less frequently, but I've heard of firms that extend such expansive claims over their employees' off-hours activities, including presuming to prohibit their employees from doing any other kind of work for pay, having a second job, running a small business on the side...that kind of thing.
My question for employees of such presumptive organizations has always been twofold:
How would your employer find out, anyway; would fellow employees rat each other out; or does the firm require to see your annual tax filings?
Your employer obviously thinks you're working there primarily, if not exclusively, for their benefit; that your paycheck is a sort of necessary evil they're willing to stomach in order to own you 24/7/365; were you a prostitute before, or is this pimp your first?
Pithy. But oh-so true. The county employees here can't do anything that the county considers "a conflict of interest." Rather a broad blanket.
This company did that too. They were a British firm, so they had a bit of a different mindset.