You're taking that in a far stricter sense than was intended for those verses. If "blameless" meant without fault, then that would contradict Scripture. In the general sense, for a Christian to be "blameless" means that they are not found guilty (with evidence) of general crimes, like those of adultery, theft, extortion, lying, or any other such thing. (Not to say someone would never lie about an elder, but that there is evidence of the crime.)
For example, since I'm in the middle of a series on Jehovah's Witnesses, when a JW elder molests and rapes a young girl, and the Watchtower protects him and allows him to remain an elder, that is violation of the Word of God. (Because they are not a Christ, so they don't care about the actual rules.)
This is not to say that a man will not have an evil past, but if he is known by the community to have been doing something that is sin, actively after he has been born again, then he is not to be put in a position of leadership. Yet, church buildings do it all the time.
For example, I can't remember which mega-preacher it was, but the guy had been caught having homosexual relations with a young man, and it was all over the news. He came onto a program with his wife, apologized (which was garbage from what I could tell), she wrote a book about her perspective and made millions in sales, and then he remained in his leadership position.
That's what it means to be blameless; there is no evidence to put blame on the elder because he has done good, and not evil, to his neighbors.