When Peter is chasing the criminal who killed his Uncle Ben, he is wearing his wrestling costume. A quick cut where Peter shoot his webbing at a crane, the camera is on him, but he is wearing his Main Spider-man costume. I noticed this on the first screening at my theater.
When I looked for it, i saw the scene you meant. At first I thought you were right, but on closer inspection, it's his wrestling costume. My DVD player has a zoom option, and it was very helpful in shedding light on it. It goes by quick enough that it's hard to determine. But it's most definitely the first costume, not the main one.
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