Where I worked for most of my career, we punched a clock. WE did not have to punch in and out for breaks though.
If you are not late, then the clock is OK. I was aghast at first, but I adjusted. Only think is, and I was always an early bird, is that one time you are a we bit late, zing! Or what used to make me laugh is the l;ine of people standing by the clock waiting for the second it hit 3:30 or 7:30 am to leave. I didn't care if I was docked 5 or 10 min pay if it meant I could beat the traffic that much sooner!
I handled one late nurse like this, she came in late every single day, and I had a 45 minute ride home and was nursing a baby...it was a looooong ride! I finally got pi$$ed and said look, if you arrive at 3:10, you get a 20 min report, if you arrive 3:15, a 15 min report, 3:25, a five min report, if you aren't here at 3:25, you can get your 5 min report from the charge nurse, cause I will be gone! She was NEVER late to work again!! The enitire unit was happy I blew my fuse! It was only b/c I was nursing, shortly after that I took a leave for 6 months to work agency closer to home until we switched to the bottle, a woman can only do so much!!
It sounds like everyone is aware of the problem, they just choose to ignore it. Why not ask the supervisor when she calls, to repaet that call at 7:30 am?? Sounds like she wants to know this stuff, so drop a line ans see if she bites. "Gee, I wish the day shift super called for report like this, maybe we would get out on time more often."