Unfortunately you are blaming verizon fios for a problem you created. Although you caught the situation in many cases the automatic payments system cannot cancel it that quickly.
I know that companies get your money faster than they refund it. I often wondered why but I guess it depends on who or what they use to process any payments.
verifying you have the funds is what you should have done. If payment was made in such a manner to avoid termination of services or to keep verizon at bay while you cover the amount it was a bad gamble.
terminating your service may incur a early termination fees or worse. So use caution before you make such a decision.