It has been established that the earliest recorded recipes of fries are French.

Which is debated as there are signs that point towards Spain having done it first.

Without knowing anything at all about the subject, except for where potatoes come from: Can we even be sure that native Americans didn’t do them first?

They did not have vegetable oil. They could not deep fry potatoes.

They could easily have used lard…

Apart from the fact that lard fries would be different from French fries (probably better, to be honest), my understanding is they fried food on stones, they did not have metal skillets with high edges (or metal skillets at all). So, fried potatoes, yes. Deep fried, no.

Your point about the frying not being “deep” is valid, but your insistence that it has to be vegetable oil is just incorrect.

Since the 1960s, most french fries in the US have been produced from frozen Russet potatoes which have been blanched or at least air-dried industrially.[12][11][13][14] The usual fat for making french fries is vegetable oil. In the past, beef suet was recommended as superior,[7] with vegetable shortening as an alternative. McDonald’s used a mixture of 93% beef tallow and 7% cottonseed oil until 1990, when they changed to vegetable oil with beef flavouring.[15][16] Horse fat was standard in northern France and Belgium until recently,[17] and is recommended by some chefs.[18] wikipedia