Even my old Micronta 22-195 will do this, with its 10MΩ DC input impedance. More expensive (better designed, often) meters have auto-zeroing which negates this, though when you get into the GΩ impedances, they struggle to cope with the stray voltages that EMI and the Seebeck effect (thermocouples use it to their advantage) generate in their front ends.
EDIT: Your UT61E+ isn't faulty, no need to worry.