If the entire DMM was floating at say 300V, there is a shock hazard. I'm not talking about the voltage
between the test leads.
A multimeter's common-mode voltage rating is dictated by the insulation around pushbuttons and rotary switch, and the battery compartment and housing screws, LCD window - any opening or seam.
It's relevant when measuring line-line voltages on a 3-phase power system, or those with a high-leg delta.
The DMM will then have a net potential wrt ground.
Also, some DMM's crash when there is a lot of common-mode voltage or noise present.
A metal foil shield inside a DMM is to help prevent this, as a DMM crash can indicate the wrong voltage or zero, which is a safety hazard.
I thought the
old 2002 Fluke 17x recall was on this issue:
"...recalling 40,000 multimeters after discovering that some of them can take up to 18 seconds to display AC voltages above 500V, possibly leading users to believe that no voltage is present, with potentially hazardous consequences."