Overtime falsification in the timesheet. How quaint. And how familiar.
I can think of at least several companies I was unfortunate to work for in UK which did exactly the same.
None of them could be arsed to pay a single penny for overtime though. So, at the time, I could not get what the deal is and why are my manager and the Human Remains droid being so persistent that I falsify my timesheet.
Being older (and hopefully wiser) now, I know that there is sufficient precedent base regarding "time in lieu" on both overtime and travel to threaten them with a tribunal case and bugger off for several 2 week holidays in a year courtesy of accrued and unpaid overtime and travel time. In order to do that you have to have it recorded, documented and acknowledged (and that is exactly the reason why they are asking you to falsify it).