That's outrageous! I think you have a breach of contract claim and likely a fraud claim. There are lawyers fighting these mugshots websites and they would love to have your fax situation to put before a court to prove the malicious intent of these websites. Get an attorney and go for it! That's outrageous! Of course we need to realize that many of these mugshots websites are based in remote jurisdictions so that they can avoid legal liability, so you may have no one at all to sue for this that you can collect from. Be sure you have a chance of recovery that exceeds the cost of the suit before you file a lawsuit and go to a lot of expense.
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I, too, am outraged at this process and agree with Bruce.
I suggest you write the second website and tell them you are going to complain to the FTC if they do not take it down. https://www.ftccomplaintassistant.gov/FTC_Wizard.aspx?Lang=en
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In addition to the answers of my colleagues, I strongly suggest having the original contract for the service for which you paid reviewed by counsel.
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