Is it reasonable for a potentiometer to have a minimum of 1.3Ω?
It's not that unreasonable, but be sure that you're actually measuring the resistance through the rheostat. Short the meter probes and subtract that reading from the minimum resistance reading. 

The parameter is called "end resistance" or ER, which includes wiper resistance. 

For example, this Indian made pot has a maximum ER of the greater of 0.1% or 2\$\Omega\$, so it would meet spec. 



In the distant past, pots sold by Radio Shack were made by a major Taiwan-based company and were actually pretty decent quality-- you might be able to find more detailed specs online.