I think I've (maybe) figured out my own issue.
The support person told me that an asset's tickets are NOT deleted when the asset is deleted and hang around as undeletable orphans in the ticket displays until 'you drop it off the back end with a maintenance job' but it seems that is not the case entirely, at least from a users's point of view.
The 'orphaned' tickets I am seeing so far appear to belong to inactive assets. I hadn't dealt with inactive assets -- we've only had MVM for a while--so all my searches had been for active assets. When I include 'inactive' in my asset search, I can find the asset that owns the (what I thought were) orphaned tickets.
Deleting the asset makes the tickets 'disappear' -- they no longer show up when one does a ticket search.
The asset and the tickets may be hanging around in the database somewhere as historical data, but from my point of view, they are 'gone' after I delete the asset, which is the behavior I was expecting.