Definitely. Heroes have been around in Peter's world for a very long time. Especially if Thor and Loki being thousands of years old counts. It'll probably come up that Peter encountered a radioactive/experimental arachnid and gained super powers as a result. From there, the hero stuff came about because Peter really is just that good a person.

Peter smiles a little sadly. "Tony wanted to know everything. All the time. He loved information. But succinct information." He shrugs. "I think actually knowing wasn't the part that bothered him. The super sudden bit of information from someone he didn't know very well who somehow knew about when it happened was probably the weirder part." A little sigh. "And I didn't do it on purpose." Had he said it was him before? Whatever. Peter did it. It was an accident. He and Tony were fine.

He sighs again. "No one ever just wants the one-word answer, man."