Also, if/when such appears, it probably won't take long for someone to develop a counter: some means of making oneself (or another person) truly believe a given statement.

This actually overstates the difficulty - you don't need to make people truly believe the statement, although that would work. You just need to make the analogues examined mimic those of someone who does truly believe the statement. I wouldn't be at all surprised to see an arms race, with artificial belief driven toward honest belief in the long run.