Why would Bobby Earl have waited till their second meeting...
...to reveal the prime evidence - i.e. that Sullivan supposedly did it, and admitted it to BE? If that was going to be your alibi, wouldn't that be the very first thing you told Armstrong?
And wouldn't a half-smart operator have seen right trhough that when he didn't?
i.e. "Why didn't you tell me this the first time we met?"
"Can't help but feel for the guy, actually." - hariseldon99 on the Norwegian child-killer