We don't know if they're "old best buddies". The only thing the synopsis states is that Harry is an "old friend", which could involve many scenarios. It could mean that Peter and Harry were friends (perhaps not even best friends) before Peter was swept away from his upper class life to a more modest working class one. Contrived? yes maybe, we don't know how it'll be handled, but it's not as much an act of sin as you seem to be making it.
Peter was left with Uncle Ben and Aunt May at age 4. After his parents died it would seem logical that all relationship and contact (or whatever relationship a 4 year old would have at all) with Oscorp would have been gone or deliberately kept from him. I also doubt Ben and May knew much if anything about Oscorp and what Richard did there. If that were the case, I'd doubt any 4 year old would be aware of their father's boss's name or their company name, so it why would even be a concern 13-14 years later?