At my station, we have a good working relationship with most of the based crews and work together, anything up to 5 minutes is usually on time. Sometimes with the shorter sectors of maybe only an hour block time, there's less 'covering up' if you like, but a few minutes in a 4-5 hour block or into long haul, becomes less signifcant even though arrival times aren't considered.
Luckily the majority of crews I work with are very down to earth and like groundhogbhx, if things don't work out but the crew are happy things have been done to standard, it's still ontime within reason.
Of course there are the few hardcore captains looking for every minute. I'm not sure most airline ops bods would want inundated with delay codes for flights departing 1 or 2 minutes late.