There is a wide variation in lead resistance, even with quality brands. Using the Fluke 8060A, I measured from 0.07 ohms to 3.50 ohms (!) on a half dozen pairs of probes. The 3.50 leads were echt Fluke, and the lowest was a set that came with an HP-Yokogawa meter.
Interesting that your DMMs were so heavily greased. Silicone dielectric grease is most commonly used for contacts that are exposed to the weather, for example, spark plug wires or lamp bulbs/sockets in wet or outside locations. It works very well to prevent the contacts from corroding together and becoming hard to remove. It also has applications to prevent flashover in medium-voltage circuits, although the DMM itself should be designed to safely absorb such events. I think if I had to restore any lubrication in the switch wipers, I would use a very small amount of contact enhancing oil, not grease.