You have a great question, but the answers given exhibit the wrong attitude. The short answer is that the recruiter likely didn't know what they were doing and

You have a great question, but the answers given exhibit the wrong attitude. The short answer is that the recruiter likely didn't know what they were doing and that you belong in a principal or management role, not in an SWE role. If correct, all this anxiety (and derogatory opinion about Google) is about fitting yourself into the wrong shaped peg, created by a stressed out recruiter who glanced at your profile for 30 seconds. How about using these CTO skills (or just being an adult/professional or big boy) and contacting them to say, "hey shouldn't my profile bring the most value in a <principal or manager>" and "look at all my skills along these lines, etc."?