Just wish we had a picture of the bill. It would probably settle this.
But the server was useless in the lack of explanation.
In the 70's I worked in a "supper club" that had a dance floor and live music from time to time. A shot was one ounce, a jigger was 1.5. (It was a premeasured cup on each end, the bigger being the jigger.)
"On the rocks" was a jigger. It was more liquor than just a regular drink, like scotch and water would be one ounce. And it cost more, built into the price.
As I recall, we figured if you were drinking scotch and water, order on the rocks, you got 50% more liquor for 25% more money. And get a glass of water and water it down yourself if you still want to. Definitely better buy.
So I am another one used to the "on the rocks" means a bigger pour. not just on ice.
(We also never served in a shot glass---the image is dive bar boilermakers to me, like in movies. For hard drinking men who want to get drunk fast, as the saying goes.)
My sister & I went to a nice bar and she ordered some drink that came with one of those 3 inch cubes of ice that had smoke in it. The drink menu detailed the liquor and ice cube, at one total price. She liked it, and when we left, she asked to put it in a paper cup, to take with. (She travels with a travel bar, and would continue to use it back in the hotel room.)
I personally appreciate OP bringing to our attention. And look what fun we have all had too.