That is not to say that the parents might not later choose to apply. Advantages would include the famously lenient Irish tax treatment of writers and artists (once entirely exempted, but now lightly taxed at 1% on annual income up to €100,000 and 2% for those earning above that figure). Eire is a good country for those who specialise in popular fiction.
Or perhaps the Republic would simply be a good place to lie low when the truth comes out. In 2006, General Sir Michael Rose called for the impeachment (a procedure not used for two centuries) of the Prime Minister, for taking the country to war on false pretences. In this context, it's worth noting that extradition from the Irish Republic to Britain has always been made very difficult. (When exactly were those Irish passports issued to the children?)
Not that the people of the Irish Republic are afraid to call people to account*; they take their religion and morality quite seriously there, still. I watched the Gay Byrne Show on 28 October 1994, when Gerry Adams faced political opponents and a far from sympathetic Southern Irish audience and was called a murderer to his face (he remained lethally calm and turned the point into an issue of good manners).
Perhaps Tony Blair, that son of Proteus, will one day be seized and held until verity is forced from him.
*The current PM is ostentatiously backing compensation claims against Libya for supplying the IRA with explosives. Could we start a leetle closer to home? How much are the IRA, PIRA and the rest prepared to pay?