The signature is just evidence of an agreement between you and the other party. It is not the only thing that matters. For example, if someone forged your signature on some paper transfer documents, would they then be able to move into your house? No.
In your scenario, it sounds like you’re worried about the third party signature service colluding with the other party and putting some terms in the contract that you didn’t agree to, while displaying the original contract to you when you sign?
If this is a genuine worry, just screenshot the document as you sign it. If the other party then tries to enforce these fraudulent terms, you can use the screenshots as evidence of the fraud. There may then be a criminal investigation, and everyone involved in the fraud may go to jail.