Ok, I checked what the code actually does and here is the answer:
1) Metropolitan admin ALWAYS gives radius 3 with no other conditions. However, you cannot BUILD it without influential culture
2) Influential culture ALONE gives a radius of 3 IF the large city option is turned on
So, to have it behave as I think it should (large cities with admin building) you need the option turned OFF!! This seems highly counter-intuitive to me.
Also, the AI doesn't take ANY of the above into account, and has absolutely no clue about trying to get radius 3 cities.
My own preference would be to do the following:
i) Re-interpret the game option to mean option OFF = no large cities (full stop), option ON = large cities with enabling buildings (ONLY), and let the building requirements dictate cultural needs.
ii) Make the AI take account of the radius increasing buildings when deciding what to build (if the option is ON). Also probably have the option being ON cause the AI to slightly more favour culture than it otherwise would until such time as it reaches influential.