As someone who was in the service back in the 80’s I can testify to what Drift said. Only service members born in the United States to American parents were allowed clearance past a certain level. This policy has obviously changed since then.
Back to the 80s, any U.S. citizen was eligible for a Secret and even Top Secret clearance. How they became a citizen didn’t matter.
The FBI background check exists to determine trust and loyalty issues.
But in an age where the top people in D.C. just dump secrets onto the Internet, does it really matter?