Mary,
I believe that advice is intended more towards larger 14 and 15" tires. There is certainly a huge difference between a 15" "Trailer" tire and a 15" passenger car tire. The trailer tire is, like the article said, designed with MUCH stiffer sidewalls to help fight sway.
If you go to the link I put up above, you'll see that most of the small trailer tire/wheel combinations there say "High speed". I never really noticed that before but there must be something to it.