The budget deficit depends upon government spending and taxes. If government bonds are net wealth, and I will presume they are, then an increase in the budget deficit will increase output. It doesn't matter which of the two components change the deficit, government spending can be increased or taxes can be cut, output will go up in either case. So the fact that a cut in taxes stimulates output and raises revenues is not surprising, anything that increases the size of the deficit will have this effect.
For example, consider an increase in government spending. This is, in part, self-financing, just like tax cuts are claimed to be. When government spending increases, output increases by some multiple of the increase in government spending through the expenditure multiplier, and this causes taxes to increase. Therefore, an increase in government spending raises taxes and helps to pay for itself. The correct type of spending on, for example, infrastructure might actually stimulate output so much that it increases revenues by more than the increase in government spending! I doubt that, but it's as easy to make this claim for government spending as it is for taxes through the Laffer curve.
Thus, the fact that revenue increases following a tax cut tells you nothing about tax cuts per se, it simply confirms that deficit spending is expansionary. Here's a graph to illustrate how an increase in government spending can increase revenue:
True or not, it's pretty easy to make these claims. Of course, we can trust the press to fact check such claims thoroughly rather than just report what they are told, can't we? Paul Krugman has something to say about that in the post that follows this one.