Whatever song they are talking about, it's not the same one as Bon Jovi's.

The one Bon Jovi used to perform and did at Evening With Bon Jovi was the Animals.

There is another one done by Wendy O Williams written by Gene Simmons and Paul Stanley of KISS in 1982. It was intended for their Creatures of the Night album. They re did it for Psycho Circus in 1998, but it again was not chosen and wound up in the box set.