Wirecut seems to work OK here, remember to check the command line options and make sure you are using the correct reference plane for the cutting.
OK, correction, if I look at the video closer and use Wirecut like you did, it does give a funky result. I never use it like that, I just press enter to cut through the objects and that works fine.
In any case I would not use Wirecut here, but instead MakeHole…
Actually, kept it at meters, but changing the absolute tolerance to 0.001 seems to have done the trick, and I think that makes sense given the circles have a radius of 5mm.
A small follow up comment here.
Both WireCut and MakeHole use BooleanDifference as part of the process, so if using BooleanDifference does not produce the desired result, then the problem is not likely to be with one of these commands, but rather with the boolean operation.