Can probing an EEPROM with a multimeter corrupt the data?
No, a multimeter putting out 400 mV shouldn't be able to erase or write a typical EEPROM.

If you observed corruption after poking at the EEPROM with a meter, it was probably due to static electricity on you or the meter.  You can easily get charged up to a few 100 V without even being aware of it.  Since your total capacitance to elsewhere is quite low, the total charge it takes is also low, and you may not even notice when you discharge yourself against something grounded.

Most ICs have diodes and other protection circuitry to be able to deal with some static discharges, but of course these only go so far.  Most current EEPROMs store data as tiny charges trapped on the gates of FETs by a insulating layer of basically glass.  These charges are very tiny, and a good zap to the chip can make a mess.