That's a very old bit of nonsense - started by Dick Armey when pushing his "flat tax" years ago as a method of trying to prevent the FairTax from gaining momentum.
It isn't true and if you'd read the bill you'd realize that.
Despite Armey's efforts, the FairTax is the tax system with widespread momentum now. Eliminated by the FairTax bill, the income tax and its appurtenances (including the records which must be destroyed) are gone when HR25 passes.
It also calls for the repeal of the 16th as an added measure but as a tax bill it cannot also be a repeal bill due to the differing requirements. There is presently a repeal bill before the House that complements the FairTax quite nicely.
Since you're concerned about the matter, you should contact your DC-folk to support both bills.