I have seen a Fluke 77 that was returned "under warranty" because the arctrician tried to measure the primary side of a 11kV distribution transformer, and just grabbed the meter, and a long stick ( some thought there) to hold the probe near the connection. Inside the case was copper plated all the way down from display to input jacks, and there was no more copper on the board, other than the copper by components under the soldering. All blown off the soldermask, leaving bare board behind. Meter did not power on at all, the Fluke ASIC was there, missing the top of the package, and the thick film resistor network was cracked, and the resistors in it had marks of flash over on them for the input side one. Fuses were intact, along with the 9V battery, and the display was still working, put into another meter to verify, as that one was there because they had broken the display. Meter was scrapped, and the broken leads were also cut to pieces. New meter sent, along with the bill. I was still in school, visiting the one place that was a RS distributor (when RS catalogues were still the only way to get data sheets or more exotic IC's, and a 2 week wait for them to arrive) and which is still running these days.
By me the distribution transformer (200kVA, is 50m away, 300m cable wise, and the cable itself probably dates from 1900 in places, being the original paper insulated cable, and the feed to me is only around 60 years old, well worn SWA paper insulated and oil filled, complete with lead wiped ends. 400A fuses by the substation, a standard size, though there are still a good number with 200A fuses, that date from the 1950's, still in use, only replaced when they blow, and they will not blow for 400A of load as evening peak, measured that one evening.
Well, that confirms my expectations what will happen when a DMM is subjected to high energy high voltage supplies like the MV part of the grid is. I don't think even a modern day Fluke will behave differently, the creepage distances inside are simply too short.
Off topic: that paper insulated cable, does it look anything like the picture below? If so, then they might not be as old as you think. Even though they have been superseded by XPLE cables, over here, production was stopped as late as 2005.
For hose who don't read Dutch, from top to bottom it says: copper cunductor, conductor isolation, common isolation, lead ply, burlap ply, double iron ply, double burlap ply.
The conductor isolation is made from paper and impregnated with oil. The burlap layers are impregnated with oil, wax and tar. At the termination point, these cables stick out of the soil vertically into the station and and are terminated in enclosures filled with oil that should be kept topped up.
The outer layer of the cable also contains chalk, but has mostly rotted away by now. It's estimated our grid still has about 50% of this old style cable in it and continues to be in service just fine. Medium voltage cables in this style can also be found with aluminium conductors instead of copper.