I I think you can strike "one of the" from your statement (and I'm a lifelong Giants fan who thinks the world of Lawrence Taylor).
People who aren't close to my age wouldn't be able to understand but from the late 1960's until the blackout rule was modified, we could only see road games on TV (in the NY market, Giants and Jets) so there wasn't a lot of football to be seen. When the Giants were home, a late game would be broadcast (back then, usually involving Rams, Packers, Vikings or Cowboys) and they would show (very brief by today's standards) highlights from early games. Back then, Butkus was either the lead highlight or he was injured. His career ended in 1973 (the year the blackout was lifted) and as prior to that, in my lifetime, the Bears were even worse than the Giants and never televised here (we played them twice at home in those years) so I never had the chance see him (or Sayers) outside of highlights and replays).
No exaggeration, he was a figure of mythic proportions, primarily due to his good (and intimidating) he was, but aided by the fact that he wasn't televised close to as much as what someone of his talent should have been.
May he rest in peace