In the UK the awarding bodies were very specific when the term "pre shift" check was changed to "pre use check". Each check by each person has to be recorded.
Certainly in the UK you can not rely on someone else checking a machine for your safety - each user is responsible for their own safety.
I am a professional trainer. The pre-shift inspections are just that. Pre-shift. One shift per day...1 inspection per day.
If multiple users are on the same truck daily, let's say, then one is assigned to do the inspection that day, and each subsequent driver, does not. By leaving a copy of the check sheet on the truck, all the users know that it has been completed. Unless the supervisor is strict enough to expect the pre shift inspection on time, no excuses, then everyone knows for sure that it has been done.
Do you have multiple users of the same truck? If so, does each user complete a check before using it, or do they assume that the guy before them did it? Is there anything that visually inidcates that the first user completed the inspection?
Daily check sheets turned in in am. and checked off with the sign-in-sheet. Info on check sheets is not specified by all, the same. At my company (corporate) they don't ask about motor oil.....Duh. But they do ask you to sign it...
When doing th circle checks, do it carbonless, making 2 copies. 1 to the supervisor and the second stays on the truck for the day. That way, everybody who runs that truck will appreciate that the check has been completed!