Thanks for that link. That document seems to be an excellent reference. I'll have to see if I can find the entire thing.
A standard DME can only accept one tuning command at a time, an agility-capable DME can accept two tuning commands at a time, and a scanning DME can accept up to five tuning commands at a time.
If I'm interpreting this properly, the scanning DME fitted to modern planes are simply capable of interrogating multiple ground stations at once, hence the pilot can select whatever DME in the cockpit, and FMS position updating is unaffected?