Three reasons: her own promises, morality and money.
1) Browne's own words are that she will "help" police and families involving crimes for free. She has been involved with families several times, not even including the Montel Williams Show. This was a high profile case about a missing child.
2) If her office can take the time to return a call then they can add an extra 30 seconds to the call, saying "Tori is being held at XYZ" then hang up. If you really are psychic and can do that then you have a moral obligation to help.
3) Here's another reason, even if Browne has no morals for helping anyone but herself. There was a $50,000 reward to find Tori. Why didn't Browne find her and take the reward money (then buy a new car or to donate it to a needy organization)? She charges $850 per call and this one could have earned her $50,000.
The likely reason Browne didn't get involved was she doesn't need anymore bad PR with her giving wrong information to parents of a missing child. Simply put, she's not psychic.
As for your claim that such a call is a dime a dozen, I don't believe that. Do you have evidence or is that just your conjecture?