In the absence of other information, I think the plain language of the offer is that night #4 is free. The bill will probably show night #4 as costing $0.00, and the other nights costing exactly what they would have otherwise cost.
If the hotel tried to charge it another way that benefited them (e.g., comping the cheapest night), I would certainly complain, as the offer does not state that they may do that.
It's not actually Buy 3 get ANOTHER free. Sunshine on Sale is Buy 3 and get the LAST night free. Here's the language from the Hyatt Regency Chesapeake's offer page...
"Book the Sunshine On Sale offer and get your 3rd night free. Offer valid May 1 through December 31, 2011"
So what they deduct at checkout is the last night, regardless of whether it was the most or least expensive. In my experience you do not get stay credit for the free night, but I have seen it happen.