I read an article about this and the concern was the possibility of a zinc component somewhere in the core, or the adhesive attaching the paper to the core. Procter & Gamble assures that there is no zinc present in the core, towel or the adhesive of their products. They are the ones who make Bounty Kitchen paper towels.
However, it appears that the most concern with using Toilet Paper, is in fact nothing to do with the adhesive but rather the fact that it has been proven that every time a toilet is flushed, a small amount of material becomes airborne. These minute moisture droplets can carry different bacteria including e.coli and do eventually cover all surfaces in bathrooms. Even though chances are slim that enough pathogenic bacteria would have collected on the toilet paper core, it is not wise to use them for your parrots.
(READ FROM : Parrots Magazine February 2013).
So I personally choose to use Bounty Paper Towel rolls for toys, but not Toilet paper rolls.