Two members of our finance committee count our tithes and offerings and record each member's (who request it) contributions because we must provide members a statement of their contributions for the members income tax. We do this because a member requested a statement several years ago to support an audit, and we did not have an audit trail to support his request. It doesn't matter to the IRS that you trust your treasurer or not. They want a paper trail.
When it comes to whether you tithe or not, that is between you and God. We personally believe that all our money belongs to God. We will always tithe ten percent, and we will contribute all we can to any of our ministries that need it. When we see the results of what we do with what little we have, we are blessed. Pinch every penny if you must, but remember that God may take you home tomorrow. I promise you one thing, you will not take a penny with you.