The rumor of Rasputin and the Russian Queen is much much older than the song though.
I don't think it was ever confirmed either. Tzar Nicholas did often leave to WW1 front to inspect troops (and other kingly duties), so it's just Rasputin and the Queen left in Moscow....
It might be bullshit. It might not be. But Rasputin's family line were dealing with said rumors for a century or more.
Anastasia survived as an amnesiac who was taught by a con-man to act like a Princess again but then slowly regains her memories before shattering the phylactery of Rasputin because Rasputin's incompetent bat familiar couldn't catch it.
You know. Once upon a deceeeeeeeemmmmmbeeeerrrrrrrrr!
4 of his great grandchildren are still around. One came forward publicly, not the rest as they mostly stay hidden since it was still taboo to admit who their great grandfather was until somewhat recently.