The verse runs

I learned that Washington never told a lie.
I learned that soldiers seldom die.
I learned that everybody's free.
And that's what the teacher said to me.

School mythology does not only idealize Washington's personal qualities, but interprets them as a metaphysical foundation of a morally and physically invulnerable nation. This would be a "lie" even if G. Washington had been a true saint.

Besides, never lying and being a morally good person are two different things. For example, the fictitious character Hannibal Lecter "does not deign to lie" - many real-life cynics served as models for him.