I don't think Islam teaches Muslims to lie. If their followers lie, its because of their ownselves.
In the bible, you will find Christians lieing. Abraham lied twice, Jacob pretented to be Esau, Rahab lied and others also but God did not ask them to lie.
We wouldn't like it if others were to then say that the Christian God asked His followers to lie, would we. They would have a greater 'proof' to substantiate their claims, after all these people were God's chosen people and you don't find God rebuking Abraham, Rahab etc for their lies. In fact, God protected Abraham and so on.
Just as a Muslim friend can turn against you, so can a Christian turn against their own kind. Pick up Andrew's God's Smuggler book, you will find a pastor there that underwent torture (his fingernails were pulled away from his hands) and still served the church. He did help Brother Andrew some (not fully because of the terrible suffering he went through), but later he did provide some info. to the government. God told Brother Andrew to tell him that he forgive this brother.
(a bit off topic: Most of us have not undergone the kind of suffering that these people did. If we were to go through it, I wouldn't be surprise if most of us end up faring worse than what these people did. )
No, we shouldn't sweep a lie under the carpet nor be stepping over one another in 'congratulating' a person for admitting that he lied. Just forgive and move on.