Following the FBI seizure of Cohen’s files, the whole truth of the Daniels payment — and any others — was likely to come out anyway. Giuliani preemptively offered several versions of that truth, allowing Trump’s supporters to choose the one they find least appalling.
He also managed to voice a confident-sounding, if wholly fictitious, rationale for Trump to stonewall special counsel Robert S. Mueller III. Giuliani knows full well the Constitution neither states nor implies that “a president cannot be distracted by a criminal investigation.” But some people who heard him make that ridiculous assertion to Sean Hannity probably nodded and said sure, that makes sense.
Giuliani is obfuscating, not clarifying. He’s making it harder to know even what the president claims, let alone what the truth might be. As a legal strategy, this would be insane. But it’s really a political strategy.