Since I’m seeing a lot of confusion about how credit reporting is done and how credit monitoring services work let me break it down a bit. Let's say you are getting a new credit card with Chase Bank. When you apply for that credit card Chase does a hard inquiry on your credit report to decide if you are elligible for that card and what credit limit they are going to give you. If they then issue you a card they then report to the credit bureaus that you opened a new line of credit with them and the limit on that line of credit.
If you have credit monitoring you would get 2 notifications. You would get a notification that a hard inquiry was made on your credit report and a second saying a new line of credit was issued to you. The point of credit monitoring isn't for the bureau to catch mistakes but for you to be aware of activity that could negatively impact your credit score. The bureau has no way of knowing if something was legitimate or not since they only have the information that was reported to them. Credit monitoring does however let you know something major happened to your credit which means you now have the ability to respond to that knowledge.
There are 2 important things to remember, all 3 credit bureaus are legally required to give you 1 free credit report per year at your request. You can get it online from https://www.annualcreditreport.com/index.action or the FTC has instructions https://www.consumer.ftc.gov/articles/0155-free-credit-repor... if you want to request it by mail. I have heard a lot of people suggest that consumers should space out requesting the 3 free credit reports so they get one about every 4 months and use that as a form of credit monitoring. It isn't completely fullproof since lenders aren't required to report to all bureaus so something could show up on only 1 report and not the other 2. The second important thing to know is that bureaus are legally required to allow consumers to dispute items on their credit report. The FTC has a sample dispute letter you can use to file a dispute, but some if not all of the bureaus have ways to file disputes online. As someone else in this thread mentioned these disputes generally require some sort of evidence that the reported item is incorrect.
So say I get a credit monitoring alert that says my address has changed because some creditor reported my information incorrectly. Regardless of any other steps I should get that resolved with the creditor because it will probably keep causing issues. But I could then file a dispute with the credit bureau(s) saying that the address is incorrect which would probably require a bill or something to prove my current address (similar to how some state DMVs prove you are a resident).