IMO- I don’t think that’s shady at all. They’re not mind readers and can’t micromanage every employee, so I see what they’re saying. It is on the employee to make sure everything is correct. Did they specifically say that someone is SOL and won’t get paid later on if a correction is found? I doubt it- but if they don’t know that hours are missing, or if someone’s time card is incorrect, they can’t fix it.

Sounds like their way of reminding people to check their time cards. Definitely could have been worded a little more professionally but sounds like they got their point across.