In general, of course he is right. But on the other hand, if you never trust, you lose out in a big way as well.
The idea here is that if you trust someone, you make yourself vulnerable to them. This is especially clear in love and romance. If you give your heart to someone (trust them completely) and they dump you, you are going to be pretty seriously sorry. If you don't fall in love, you won't be open to that kind of stuff.
But staying closed off and not trusting carries its own price -- you lose something of being human if you try not to have close relations with other people.