But you must know that the moment anybody proclaims that they know that this or that teaching is wrong they set themselves up as rejecting untruth and lies because they know or at least have a feeling for what is true and good. Even if a person does not claim that their denomination, church, meeting or whatever is right and teaches the truth they nevertheless make an implied claim to knowing the difference for themselves. There's no escaping this tendency to make judgements so one might as well make judgements that one is prepared to live with and not change from year to year or month to month.
Your first two sentences don't necessarily follow from each other.
If I believe that Pastor Joe Blow is teaching untruth then it doesn't follow that I make any claim, actual or implied, that the church I attend is right and truthful in every regard. All it means is that I regard my church as being sufficiently close to the truth to be acceptable to me. Essentially what that means is that I think the church is right (or acceptably close) on the things that are important while not necessarily taking a stance on the things that are less important.
I believe that an important part of the process is coming to a decision regarding what is critical, what is important and what is unimportant. For example, my church is a much older congregation than I would choose but that's not an important element so I can live with it. There are a few things in the traditional of the denomination that I'm not entirely in agreement with but it's not critical to follow every part of that. The parts that are critical, which essentially boil down to the nature of God, Jesus Christ and the Holy Spirit, are areas where we agree so we're good there.
Most of the teachers I personally reject as being false teachers are those who I believe deviate from the critical areas of the faith, by either diluting the significance of Jesus Christ, by presenting a god I don't recognise or similar.