No it doesn't. That's a pretty ridiculous claim. At least in the games I run and play in, you can't count on a short rest conveniently arriving when you want it. Sometimes you have to work to make it happen. And that's good! That means the pcs have to use their noggins, have to strategize and plan and work to take advantage of the environment or set up conditions to allow for a rest. Might be as simple as "We close the door behind us and rest in a sealed room" or "I cast rope trick", or it might require backing off, retreating to a safe space a mile outside the dungeon, setting up an alarm spell and some quick hunter's traps, and concealing the whole thing with brush. Short rests aren't always easy, or even possible, to take, but - when a group has this issue, do the pcs actually do anything to try to get one, or just assume they can camp in a busy hallway?
Sorry, the short rest issue is one that is starting to trigger my rants.