I know what number you are talking about, and you are right, it is different from *67- which just hides your number.
There are some services you can purchase from your carrier that would make your number an invalid one, like this one did. You can purchase the feature on a monthly basis and then use it when you want using a code. The number that shows up should be traceable though, back to the company. It will just give you some service code.
I had to use this when I was dealing with an ex and got a new number but for legal reasons had to contact him.