Just plane smart is not a typo, it's just one more punny phrase coined by/for American advertising. As you may have guessed, the slogan is owned and used by an airline; Southwest Airlines to be exact.
The association between the slogan and the airline was not always a given. In 1992, shortly after Southwest started using the slogan, another airline claimed prior rights. Stevens Aviation had been using the shortened form, "plane smart" since the 1970's.
Normally, this kind of turf war leads to a lengthy and expensive legal battle. At the suggestion of Stevens Aviation, instead of a legal pissing match, the dispute was resolved by an arm wrestling match between Southwest's attorney Steve Kelleher and Stevens' Chairman, Kurt Herwald. The outcome was decided by the best two out of three rounds, with the loser of each round paying $5000 to a charitable organization.
The wrestling match was accompanied by lots of free and positive publicity, and ended up a win for both sides. Although Southwest lost the match, Stevens decided to let Southwest continue to use the tagline.
As Slashdot hints, there may be a lesson to be learned here for enterprises all over the world engaged in gruesome and unpleasant litigation.
My first source of information on this event was Slashdot:
I gleaned some details from these Web pages:
Loads more information is available by using Google
on the tagline for the contest: Malice in Dallas