That is essentially correct. The Federal Motor Vehicle Safety Standard 49 CFR 571 has several sections relating to tires. Section 119 applies to non-passenger vehicle tires, including motorcycles. If you want to bore yourself you can link to all the various standards from here.
http://www.gpo.gov/fdsys/granule/CF...1-title49-vol6-sec571-119/content-detail.html. Here the link to a pdf of Section 119.
http://www.gpo.gov/fdsys/pkg/CFR-2011-title49-vol6/pdf/CFR-2011-title49-vol6-sec571-119.pdf
In a nutshell the FMVSS requires that rims and tires be identified for the use they are designed for. Passenger car tires and rims are not designed for motorcycles, hence cannot be marked for m/c use. The only reasonable way to meet the standards is to design tires specifically for m/c use and then identify them as such. There is one major difference between the requirement for m/c tires and car tires. Car tires must have wear bars at 2/32" tread depth. Motorcycle tires must have wear bars at 1/32" depth. IOW, m/c tires are allowed by law to wear down 1/32" more than are car tires.
I do not find anything in the code that prohibits using a tire for a purpose for which it was not originally designed and manufactured. As far as I can tell no tire dealer, or m/c dealer, is prohibited from mounting a car tire on a m/c. There is a requirement that every new tire be registered but I don't find any specific requirement that the vehicle the tire is installed on be reported.
What is really needed is a code update to recognize the tire requirements of non-leaning three wheelers like the Spyder.