Is true that the if I can show that I can't pay my taxes, the IRS has to settle may tax bill for less than the full value?
Would that it were…unfortunately, while you have stated one of the grounds on which the IRS may settle a tax debt for less than payment in full, the IRS is not obligated to do so. Instead, whether or not you can get your tax liability reduced depends on the outcome of an IRS debt negotiation—i.e. you need to convince the IRS that it's in their interest and/or the interest of simple fairness (yes, the IRS does try to be fair) to allow you to settle your debt for something less than full payment.
A favorable IRS debt settlement is called an Offer in Compromise or OIC. The three grounds for it are:
However, it must be stressed that the bar is very high: the IRS does not like accepting less than full payment; and since they don't have to, the taxpayer must be very persuasive to have an OIC accepted. Experienced tax counsel can help you understand if getting an OIC is reasonable likely, as well as maximize your chance (such as by negotiating with the IRS) of a successful outcome.