This one is even weirder to me. If it is best effort then this means that it is okay if the work doesn't get done. If that is the case, then why can't it be done the next morning?
My team has an "oncall" shift like this where we assign a person to be responsible for triaging bugs and other non-urgent alerts just so we don't all stare at it and wait for somebody else (or inevitably me, the lead) to handle it but they are explicitly told that this responsibility does not extend beyond working hours.
I do bring my computer with me when traveling out of state when on call but generally don’t worry about e.g. going for a few hours hike or whatever even if I won’t have the laptop with me. If it were stricter it would definitely be more annoying…