I'd be willing to bet that the problem is the work isn't getting done. I've seen this many times now. No one is going to care how much you time you spend walking your dog if you're getting your work done - you only draw attention to yourself when you're lacking, and then your manager starts looking for reasons, sees you work 20% less than expected, and then what would you say? You'd call them on the carpet, too. I'd give them a part time job since that's what they seem to be capable of.

I've religiously filled out time-sheets, in various forms) for 30 years, and I don't think they have been looked at more than a few times by my managers since my work gets done, and more. But I know for damn sure the laggards get scrutinized.