Apparently, stretcher patients aren't the only bulky thing being moved around the ship:
^This cute hovercart would easily fit inside a turbolift...
^While this one would not.
Perhaps there exists an alternate transporting system for long, low items such as these pallets. Say, the corridors in TOS are very high, with lots of empty space atop the heads of our characters. There might be futuristic invisible trunkage up there: not just dataways or magic power flows, but a gravitic tube-mail sans the tube... Doesn't explain the arrangements of the TOS movies or the TNG era, though.