My point was very much the same as yours but from a different perspective.
I would suspect that most people take the "under 1 MOA all day long" as a boast intended to give the impression that all the groups will always be under 1 MOA.
Based upon your posts over the years, I recognize that you have a very wide range of experience and you naturally include that knowledge in your interpretation of the " all day long" statement. I'm not sure everyone does.
I was trying to say that even a sub-MOA rifle doesn't shoot necessarily sub-MOA all day long and, almost guaranteed, doesn't shoot every load the same.
That is indeed why we hand load and tune loads for performance.
A sub-MOA achieves that 'on average' and even within a particular load there can be anomalies.