I was going to comment on how ohms are measured, but SBprojects beat me to it. In integrating DMMs, it is a simple task to integrate with the unknown input resistor, and de-integrate with the known resistor. So the only trick is to make sure that the input common mode range of the A/D is not exceeded by the voltage across either the reference or unknown resistor. SBProjects also correctly pointed out that you can get the Siemens ranges just by reversing this process. This allowed measurement to very high resistances (inverted) but resolution went down as resistance went up (or Siemens went down). The 200/2000megohm ranges in the 8060 just made a Siemens reading and reciprocated it to get it back into ohms.
The protection afforded by the PTCs can only be used in Ohms circuits, because the very noisy voltage across the PTCs is not measured. An advantage of ratiometric ohms conversion is that it only requires the reference resistor to be precise. Any other voltage, including the VRef is not at play.
The main down side to radiometric ohms conversion is that it does not lend itself well to four terminal ohms measurements. Although theoretically possible, it would pick up a lot of noise. All meters I am aware of with four terminal ohms connections, use constant current measurement techniques.
As far as the ohms protection clamp goes, the old way of using back to back zener connected transistors (usually 2N3904) dates back a long way with Fluke. I first saw it used on the 8020 meter, but I suspect that older Flukes used it too. Bob Pease had an article on this. The main reason for using transistors instead of Zeners is that it makes an extremely low leakage clamp, usually less than 2pA. This was required for the Siemens ranges. Fluke used selected 2N3904s for this way back when. I touched on this in an earlier post.
I also concur with other posters that the switch resistance on the current inputs is negligible. It only very slightly contributes to burden voltage, and the fuse would be a far larger contributor to that. Note that the high current range does not go through a switch. Certainly the sense voltage does, but any series resistance in the sense lines could be very large and not affect the accuracy until you hit a point that leakage current becomes an error.
The 8060 used dual trimmers, a fine and coarse trim. These trimmers were selected for Temp-co and were highly evaluated for long term stability. It also had a primitive constant current source, but that was only used for the diode check.