The Washington Post addresses the Trump's word against Cohen's argument you make. In this case, it's not one person's word against the others. There are witnesses and physical evidence.
In case you doubt the strength of the case: Did you notice all the other people implicated in Cohen’s plea? There is “Corporation-1,” presumably American Media Inc. (AMI), which owns the National Enquirer (“Magazine-1”). Members of Corporation-1 (including editor in chief, or “Editor-1”) would presumably have information and be able to corroborate Cohen’s account regarding the Karen McDougal payoff. The information document filed against Cohen also notes the existence of a text between Editor-1 and Cohen, corroboration of the arrangement to pay off a second woman, presumably Stormy Daniels. An encrypted phone call is also mentioned, as is an attorney (one more witness!) who represented both women. And let’s not forget the “executives of the Company” [Trump’s] who “grossed up” the reimbursement to Cohen; that’s two or more additional witnesses. We learn that “Executive-1” received the request or reimbursement and shared it with more executives. More witnesses. In Count 7, Cohen is accused of enabling Corporation-1 to make an illegal corporate campaign donation. That means the company and/or its executives might have liability as well. Count 8 mentions campaign executives (who might they be? how many?) who worked with Cohen to effectuate the scheme.
In sum, it’s not Cohen’s word against Trump’s, but rather a raft of witnesses whom prosecutors have or will be able to talk to (some to avoid liability of their own) and documents as well. There is, in short, a ton of evidence out there concerning the campaign finance scheme to make sure two women didn’t mess up Trump’s chances of getting elected.
