Most Christians seem to believe that it was because Moses struck the rock twice, instead of once, in so doing lacked the faith that the Lord would release the water with just the one strike, but you are correct, it had nothing to do with striking the rock with Aarons rod, and everything with what Moses said, as revealed in the GNB, Psalms 106: 32-33; the people made Moses so mad with all their complaining, they made him so bitter that he spoke without thinking and was in trouble because of what he said.

And what he said is found in Numbers 20: 10; "Listen, you rebels! Do we (Moses and Aaron) have to get water out of this rock for you." In that, they stole the Lord's thunder, for it was He and He alone, who had the power to bring water from the rock.

May our God preserve you John.