Well, you could have them install the ONT on your home's exterior, then install your own run of plenum CAT 6a from closet to the ONT's location. Otherwise, there's not much to do but tell them where you want it mounted then sit back and watch.
Also, FO cable is much smaller than even twisted pair. Easy to run in locations that might not be so for other types of cable.
Ditto what dogmush said. It will be fiber to the ONT, then twisted pair to downstream devices.
I know you have a burr under your saddle about the install, but from hard-won experience you really really want the ONT next to your connection locus. It makes things much easier in the long run. You can always specify cabling route to the installer, then let them know you are very picky about workmanship. Sometimes it has good results, sometimes not. They may charge a little to run an unusual route but, unless the cost is exorbitant, it's money well spent.
Brad