I think what the OPs mean is that in the classical case, the lone, noninteracting particle has a fixed, definite energy and not an average energy. There are no other configurations to consider, besides the set of points that the particle may be in space, but that is irrelevant to the energy and temperature. Maybe what you're saying is true if you consider a single quantum particle, I'm not sure.
I don't think invoking quantum mechanics is necessary here honestly.
Let's say I flip a coin; most people would model the outcome as a p = 1/2 chance of heads and p = 1/2 chance of tails. This is fairly standard, of course, but I think it illustrates my point.
Of course, in reality there is only 1 outcome that's going to happen, but literally the best model of the system we can come up with, given our ignorance, is that it's 50/50 heads and tails.
So, what I am saying is that given that we know relatively little about the particle --- what it's average energy is --- we can come up with a probability distribution over states with that average energy that represents our "best guess" or "least biased" probability assignments.
