He had to buy it because to be able to make these claims the company has to be ok with it, and you sign a contract. These contracts often have provisions that say that if the company is lying about its users, it’s revenue etc then the deal doesn’t go through. Musk tried to say that twitter lied about how many bots there were, and not go through with it, but the contract he signed said basically “I have decides to buy it regardless, so I waive my right to due diligence” and bob’s your uncle.
There wasn’t a verbal contract, very much a written one (but you’re right that even if not he’d probably have been nailed for fraud anyway)