“A man who’s true to his word, / there’s nothing he needs to fear. “The Green Knight says this to Gawain after he reveals how Gawain has...

Sir Gawain and the Green Knight is a
medieval romance.  It is escapist in nature.  It's not supposed to be realistic.  It is
anything but.  The work is idealistic, filled with the imaginary, created, chivalric
code common in medieval literature. 

Works like this one
don't include characters that are like actual human beings.  No society ever lived under
the chivalric code.  It is imaginary.  It is the stuff of
legend.

The line you ask about is tremendously idealistic. 
It presupposes that no harm can come to a truthful person.  It is the product of an age
that still believes in an ordered universe (at least in its literature), in which right
always triumphs over wrong and good always defeats
evil. 

In short, the line is idealistic, wishful thinking. 
It couldn't be more wrong.  History demonstrates that men, whether or not they are true
to their words, have plenty to fear. 

Gawain
is, however, considered a step toward more realistic, less idealistic
literature, though the line you ask about doesn't suggest that.  Gawain is a very early
example of a hero that actually has faults.  That's rare in medieval romances.  As such,
it is a forerunner of literary things to come.