You are understanding that correctly.
I have no idea if the volunteer background check would show the LTC, nor, if it did, if that would be reported.
But once you become someone 'under their control', even as a volunteer, they get to set the conditions. Their control is limited to what you do, or do not do, as a volunteer.
'Is it a legal matter' if you don't obey their conditions? I don't know. With LTC, if the condition you disobey is to carry, the behavior itself is not illegal, unlike, say, doing drugs on a field trip with the kids.