It still appears to me that the difference is "I believe that This is true, and I don't think That is true.* Therefore, This is allowed, but That isn't." You have denied this, but everything you have said-- particularly how you have decided to call acceptable things "facts" and unacceptable things "beliefs"-- fully supports this reading.
*You can, also of course, change this to be "I believe that This has good reasons to support it, but I don't think That has good reasons to support it. Therefore, This is allowed, but That isn't." "Good reasons" appears to be how you distinguish "fact" from "belief", and therefore determine "truth".