I'd be interested to see that schematic.
I have one of these probes and it works well. The only snag is it's easy to leave them switched on, so if you don't use them often, take the battery out. They're often available much cheaper than the Tek branded ones, because ebayers don't realise they're the same thing. Though perhaps there is a difference : according to that video, it rattles and the Tek one doesn't. Mine rattles too. Maybe the tek one has a little bit of goo in it to stop it.
I have an almost identical probe (type E14), also made by Chauvin Arnoux, apparently for a 3-phase analyser that they sell. (That rattles, too). It's only marked as AC and has no zero adjustment. However, I think it has exactly the same hall-effect measurement system because it has a bandwidth that's more or less flat down to about 1Hz. I think it's the same thing, but with a DC blocking capacitor and no zero adjuster.
Since AC current probes are always cheaper than DC, especially secondhand, there's a bargain here if you don't need 0Hz. It may even be possible to remove the capacitor, add the pot, and operate it down to DC.