To the OP: I don't think there'll be a problem with the Lithium 9V cells on your meter either. I use lithiums on several meters, but never used 9V on them given that historically I had one, perhaps two accidents.
On the other hand, AA and AAA problems are very real - having lost several new and irreplaceable equipment over the years, I use Lithium cells on the most valuable ones. I don't use rechargeables as, in my use case, they become a burden to manage charges, etc. (Too many gadgets, kids toys, etc).
I have noticed that the chance of alkalines leaking are with equipment with a standby mode that slowly discharges the battery over time, as well as equipment that is subjected to mechanical abuse (flashlights, for example). Most of the stuff with a mechanical ON/OFF switch seems to preserve the batteries for a lot longer.
I too had the offending leaking batteries on their original packaging. I wonder if they were stored improperly or subjected to mechanical abuse.