If I can put up with work getting in the way of life (on call, no overtime pay, etc) employers can put up with life getting in the way of work (appointments, off topic research, etc).
Nine times out of ten it ends up helping them too. The research ends up being mutually beneficial. A healthy me keeps coming to work. The list goes on.
I just try to be honest and reasonable about it. So far they have too. Please let me know what needs to be done, and it will get done.
Company time only exists when the company is paying for time, salaried employees are filling a company role not being paid for any specific period of time. If the company gets too specific about what time belongs to them they risk losing the exempt part of salaried-exempt and would owe back pay for any time over 40 hours that you may have worked.
Another wrinkle is most workers aren't really aware of the legalities of salaried work, you'll see people making statements like the OP here about "company time" for example. Originally the arrangement was designed for people like CEOs and executives of companies where it wouldn't make sense to track hours as they had a stake in the company, but it has been expanded mostly to side step things like mandatory overtime pay.