—1 Timothy 5:1-2 (NASB)
So you absolutely, without a shadow of a doubt, beyond all attempts to argue to the contrary have the Truth on your side. You're right, they're wrong, there is no gray area whatsoever. So how do you broach the topic with another believer? How do you "slap them down" with the absolute Truth to put them in their place? Well, it's not a license to "sharply rebuke" anyone, but an opportunity to prove the quality of your own biblical love in how you choose to behave.
I do think it's important to make the distinction between correcting a fellow believer and dealing with a false teacher. Jesus Himself dealt very differently with those espousing false doctrine than with those struggling with personal issues of sin. For the good of all, false teachers need to be loudly and publicly denounced, but that's not the same treatment warranted for personal relationships. Even the necessity of reproof or discipline is to be guided by Christ's commandment to love one another. I would submit that at such times the true quality of our love is revealed.
Someone recently admitted that they feel that because of the numerically superior presence of their own personal flaws that they feel inadequate to address the flaws they see in others. Well let's keep in mind that addressing "flaws" is the wrong application if you've arrived at the brink of issuing a sharp rebuke. It can only be an issue of sin or doctrine which can be addressed; everything else is a gray area we're supposed to live with. Just as our parents and family aren't perfect, yet we love and put up with their eccentricities, so it's to be within the family of God as shown here.†††