With a 1:1000 divider and 1 Gohm for the input the output resistance for a simple divider would be around 1 Mohm. This would imply some 1.1 M internal to be supported by 10 M from the DMM.
So I don't see why it should make that much difference if the meter is 10 M, 11 M or possibly > 1 Gohm. The high Z meter would give some 10% too high, but not off by that much and especially not too low.