Will Buying "SIM-Free" iPhone from Apple Work on Verizon
There are two different iPhone 5s models sold in the US -- the CDMA model for Verizon or Sprint (which also supports GSM connectivity for international use) and the GSM model. The unlocked phone is the GSM model, so it won't support CDMA and won't talk to Verizon's network (except perhaps for data (not voice) on 4G/LTE, where Verizon uses GSM like the rest of the world). So you can buy an unlocked phone and put a Verizon SIM in it, but it will at best only work with Verizon for data, and only in areas where they have 4G coverage.

Just look at the bottom of the page you link to in your question, where it says:


  If you buy a SIM-free iPhone, you will need to purchase a
  GSM-compatible nano-SIM card separately. In the United States, you can
  purchase such a SIM from AT&amp;T or T-Mobile.