Can you cook pickled onions

Well, you're definitely right. Onions cooked at a high temperature act differently than ones cooked at a low temperature, per "the bible" aka On Food and Cooking. However, it doesn't go in to much of an explanation as to why. Probably the most relevant aspects of what is in there are:

When onions and their relatives are heated, the various sulfur compounds react with each other and with other substances to produce a range of characteristic flavor molecules. The cooking method, temperature and medium strongly affect the flavor balance. Baking, drying, and microwaving tend to generate trisulfides, the characteristic notes of overcooked cabbage. Cooking at high temperatures in fat produces more volatiles and a stronger flavor than do other techniques. (p.311)

Since a low temperature produces less volatiles, I assume that the natural sugars of the onion shine through instead.

It's probably also important to understand where the oniony flavor comes from. The spice, as you describe it, is the onions natural defense mechanism. However, it doesn't exist defacto in the onion, but is rather the result of a chemical reaction. The onion stores very reactive sulfur in the cell fluid, and a seperate trigger mechanism in a storage vacuole. When you cut / crush / cook/ peel the onion, you break the vacuole and the enzyme and sulfur cause a chemical reaction giving off the spice. (p272 & 310)

Onions have a lot of sugar in them. All they want in the world is to burn and fill your kitchen with oniony smoke.

The solution, as with all things heavy in sugar, is to turn down the heat and stir frequently.

That said- if your olive oil was extra virgin then it might have been your oil that started burning before the onions did.