I see your point about Rout 13 being just on the Swiss side of the border. However, E43 appears completely inside the Liechtenstein side of the border. I can visualize this road as having significant traffic, which makes its use inexplicable. However, there is no other single road which can provide a north-south (or south-north) route.
On Google Earth, the E43 (green sign) appears to be the Autobahn on the Swiss side of the Rhine. The 13/A13 (Blue sign) appear to be the pre-Autobahn highway in that area of Switzerland, sort of like the parallel US Highway 80 and Interstate 20 in my part of the world. Across the Rhine from northern Liechtenstein, the E43 has another 13 sign on it, this sign in in orange. So there are two different 13 signs, one in blue and one in orange, but not on the same road. If that makes sense.
On GE, there are no highway numbered roads in Liechtenstein, they only have street names. My proposed route is the 191 (blue sign) out of Feldkirk to the boarder. Then the same road is called Feldkirkerstrasse. Further south around Schaan, it becomes Landstrasse all the way through Vaduz and to Balzers. West and Southwest of Balzers there are two bridges across the Rhine. One on Gagoz (street/road) and the other on Rheinstrasse (street/road). Both bridges connect to Tubbach, Switzerland. Tubbach is maybe a mile north of Sargans, where we know Kisha/Jen boarded the train for Zurich.
Liechtenstein only had a population of about 30,000. I, personally, wonder just how high the density of travel on those main roads are. There are a couple of more remote border crossings in the far norht of Liechtenstein, but it seems to me to be problematic getting teams to them, to start the moped ride. The Highway 191 crossing only appears to be a couple of miles from the Feldkirk train station. Maybe Neobie can clarify, since he had boots on the ground there.
In the end, it just depends on what production wanted to do anyway. They are going to have to have space for a lot of people and vehicles where ever they start and stop the moped ride. It appears to me that the other team member and film crew travel along in a van to the other end of the ride. So production will have lots of crew for this little show.