This theory is that Madeleine was actually found alive, but her case had become so high profile, the lie that she was still missing had to be upheld for her to be able to live a normal life.
Even if Maddie was given a new identity, any girl her age spotted with the McCanns or that looked like her would be constantly hounded by the public and press, so the only way for her to be able to live a 'normal' life would be to fool people into thinking she was still missing.
