It's a little bit more relaxed than "no commerce allowed".
Communications in which the operator has a pecuniary interest are prohibited[1]. But, personal communication with a business is allowed. Ordering a pizza via phone patch is allowed but soliciting orders for your pizza shop is not.[2]
There are other issues that would make connecting to the internet problematic that are prohibited by §97.113. Things like cryptography, obscene or indecent words or language; false or deceptive messages ...
1. https://www.law.cornell.edu/cfr/text/47/97.113 §97.113(A)(3)