My parents started making tuna fish salad sandwiches this way years ago, and as far as I’m concerned theirs is the best and only way to make a tuna fish sandwich.
First it helps to start with high quality canned tuna. If you have leftover cooked tuna steaks, then by all means use them instead of the canned tuna. Both Trader Joe’s and Whole Foods have excellent canned tuna packed in olive oil. (The brand I like at Whole Foods is Wild Planet.)
Tuna packed in olive oil may be more flavorful than tuna packed in water, but check on the quality. It may be better to use tuna packed in water, drain it, and then add a bit of your own high quality extra virgin olive oil. This requires a bit of experimentation with brands.