This will be the key...if you can prove the contractor lied? Then you can refuse to pay the full amount.
But you would have the burden of proof
law, if two parties agree to the terms of a contract, and one party complies with their part of the bargain? The other party can compel them to do their part.
So, in the case you describe, if you had an agreement to pay for services, and services were rendered as agreed? You have to pay.
That is basic contract law...
However, contract law also provides that both parties are required to "negotiate in good faith"
So, if one party lies to another about a material matter ? That can be grounds to void the contract
1. Say that A agrees to build B a structure. A is not sure what it will take to complete the project, but reasonably believes that it will require a particular procedure. And so A makes the quote based on this belief. B agrees. A starts to work and realized that the procedure is not required. A completes the task. B is on the hook for the agreed cost. The fact that A "got lucky" in the estimate is not grounds for B to void the agreement.
2. Similar example, but this time A believes that he will NOT need to perform the particular procedure. But he lies to B and tells her that it will be required. Same result in the process...A completes the task, no procedure used. In such a case, if B sues and can prove A lied? Then B can have the contract void. B will still owe A some money (since the work was done) but the amount would be determined by the court based on the reasonable amount related to the actual work done
So there you have it....the closer your case is to #2 above, the more likely you would be to win if you had to go to court.
The key will be what you can prove the contractor knew at the time and what the contractor told you....if they lied to you? You can ask the court to reduce the amount you owe.