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I have a similar situation (mine was from BonTon store card 2006)...they didn't show up on my report, but they've sent me letters and I saw two HP from them during my rebuild. Are they on all three reports? Did you try a dispute via CRA?
You can send a DV, but in view of your phone converstation, they will most likely verify based on their records of an asserted debt due to Dish Network.
Filing of a dispute under the FCRA requires some basis for showing of an inaccuracy. "Sure I paid the bill" is a bit lacking in substance, and verification will likely occur in response to a dispute the same as if you send a DV.
They can attempt to collect until the debt is determined to be invalid, which would most likely require bringing civil action and obtaining a decision by a court.
You can wait for the colleciton to become excluded, which must occur no later than 7 years plus 180 days from the DOFD.
Until them, they can continue collection activities and their credit reporting will continue to appear in your credit report and your scoring unless you get acceptance of a PFD offer.