Would the dentist really lie to me about this?

No he wasn't lying to you. Wisdom teeth tend to cause cavity on themselves as well as surrounding teeth because they are difficult to get to. The older you are the harder they are to get out. On a lot of people they tend to get impacted or shift other teeth. You can't always see a cavity with your eyes unless you know what to look for. But black? It should be pretty obvious. And by saying the xray looked fine, do you know how to read them?