As both an IT Director and Security Director for the company I work for, I can tell you that at least in the US this sort of thing is a pretty common requirement for someone in your position. In fact I've even seen retail establishments where they had little or no CCTV coverage of customer areas, but lots of cameras covering employee work areas for just that reason.
Over reporting your hours is a form of fraud, and as such "Employee Handbooks" and other corporate policies and procedures go out the window as far as CCTV and privacy are concerned, because the business is now investigating a potential fraud committed against them.
For the record, I've never actually heard of someone being prosecuted for 'payroll fraud' at any company I've worked for, but I've seen lots of people get fired for it.
The way I look at it, it's one thing if someone is coming in a few minutes late, but when you have people coming in 20 or 30 minutes or even hours late, and claiming the same pay they would earn had they actually worked those hours, it's a crime and the employee should not be surprised if it results in their termination.
In simpler terms, most employees are compensated based on the hours they work. If they are lying about how many hours they are working to get more money than they've actually earned, they are stealing from the company.
So my advice is do what they're asking, because they have every right to ask.