How could a "simulated outdoor recreation area" pose any significant budgetary constraints? It's not like they need to build sets. Drive 15 minutes to Griffith Park and film! (unless the constraint was the cost of the location shoot). If necessary, construct a simple arch like in TNG. They wouldn't even need to show it opening to the corridor. Shoot someone entering from the side, then cut them emerging from a door. Also, given this info and their appearance in TAS, can we finally put to rest the notion that holodecks were non-existent in TOS?