Fortune 50 Company Rewriting Pop Songs

Dear Rich: The company I work for -- for-profit Fortune 50 -- has been creating songs as learning tools for its employees and clients' employees. These adapted songs keep the tunes of popular music and simply change the lyrics to fit the subject matter.  Does this fall under parody? Or would this be a copyright infringement if the company does not ask or get permission from the original artists?  If the company is recording or performing copyrighted songs without permission, it's infringement. If the company is simply rewriting the lyrics and encouraging others to sing it to a certain melody that may be an infringement (as we discussed recently). Lyrics are separately copyrightable and if the company is borrowing too much from the originals, they would create an infringing derivative.
Are these parodies or fair use? We doubt whether the changed lyrics qualify as fair use/parody. Most judges believe that a parody of a song makes fun of the underlying subject matter (although one judge claimed a parody doesn't even have to involve humor). In any case, if the use is commercial, and the company is recording or performing the complete song, this would be a hard sell as a fair use defense. In addition, the Fortune 50 classification and the accompanying deep pockets also make the company an appealing target ... should the song owners learn of the infringement.
By the way Dept. Permission is not required from the original artists; it's required from the owners of the song copyright (usually a music publisher).