You're spot on. Bartender just didn't know.

Olive brine (or juice)
Tequila
Lime juice
Optional orange liquor. I prefer orange bitters

Shake, strain over a fresh sliced jalapeño, serve. Garnish with olive. Or jalapeño. Or both.

Unfortunately this is why you need to know the ingredients and measures in the cocktails you prefer to drink. Some people hear the word daiquiri and all they think of is hurricane glass filled with a frozen strawberry or banana drink. There's plenty of bartenders out there that don't know how to make a proper martini or old-fashioned. There's plenty of them that think sour mix is what goes in a proper margarita or whiskey sour rather than freshly squeezed juice.