Why does HPV Infect Squamous Epithelial Cells and Not Others?
The answer usually lies in whether the cell of interest expresses the correct receptor.

Check this:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2820467/

This excerpt from that review explains why:

"Although both the α6β4 and α6β1 heterodimer were capable of binding VLPs in vitro, only the former was supposed to function as a HPV receptor, which was concluded from the results that the α6 subunit associated preferentially with the β4 in epithelial cells [12], and the α6β4 complex was expressed exclusively in the basal cellular layer of the stratified squamous epithelium [13], which was presumably the only site of productive PV infection"