Google had been a dominant search engine for years before they went public, and I can't imagine they turned down many $50 billion funding rounds simply to avoid turning public before their IPO.
The Securities Exchange Act of 1934 sets forth certain requirements for companies to register their shares with the S.E.C.
Specifically, Section 12(g) requires that a company register its securities with the S.E.C. if it “has total assets exceeding $1,000,000 and a class of equity security … held of record by five hundred or more … persons…”
Sounds to me like this law has been around for a while.