Yes, and Bose Einstein statistics can be obtained either by assuming indistinguishable particles, or that this probability distribution fluctuates uniformly. No

Yes, and Bose Einstein statistics can be obtained either by assuming indistinguishable particles, or that this probability distribution fluctuates uniformly. No experiment can decide between these explanations; the physics comes out the same. These are two stories to go with the joint distribution, which is what we actually observe. One could wonder why we need "thought glue" at all to explain particle physics in the language of human-scale physics. The joint distribution is what it is. No need to accept the second story; there are likely others. But one is entitled to roll one's eyes when hearing about indistinguishable particles.