At the moment any permissions/claim mods will prevent the block breaking as a unknown fakeplayer is being used.
If it would use the game profile of the player who placed it, like other mods do, this wouldn't be an issue.

We simply reuse the generic fakeplayer provided by forge instead of creating a mod specific fakeplayer. Trying to track the actual player is simply to complicated and prone to many issues. E.g. it would be affect by chunkloading order and similar.

As it is the generic fakeplayer, either the permission plugin should take it into account or ideally should help forge to provide a best practice approach to make it easier for everyone as well as ideally deprecate anything which should be avoided.

Can you tell a few of those other mods to get a reference?

dan200/ComputerCraft#518

I didn't notice any issues with EnderIO, ThermalExpansion and few other mods with block placers/breakers so I assume they all do the same.

CC, TE and EIO incorporate ownership in their machines afaik, where AE does not .. I am not sure how tough it would be to integrate something like that, maybe take the player from a biometric card in the security station