Jennifer Lopez -- Happy Birthday Ambush in Turkmenistan

Jennifer Lopez did nothing wrong when she sang happy birthday to the President of Turkmenistan ... because she was AMBUSHED ... this according to her rep.

Mega-manager Benny Medina tells TMZ ... Jennifer was NOT in Turkmenistan to perform for the Prez -- she was hired by the China National Petroleum Corp. for a corporate concert. Lopez sang 3 songs, and Medina says as she finished her set someone walked up to him and said President Gurbanguly Berdimuhamedow was in the audience and asked him if Lopez would come back on stage and wish him happy birthday.

Medina says it was HIS decision to bring Lopez back on stage at the end of the concert. Medina tells us ... the Prez got on stage and the M.C. started goading Lopez to sing "Happy Birthday" -- singing it quietly in her ear, goading her on the spot to sing the Bday song.

Medina says there was no reason to do heavy research into the President's record, since no one even knew he would be at the concert. Medina adds when Lopez started getting flack he did some research and found the FORMER Prez is the one with a record of human rights abuses, and Berdimuhamedow actually seems ok.