I assume you are asking about a 12 Volt, not amp (amperage) ground connection.
Electrical problems are frequently caused by a faulty ground which is generally caused by corrosion. Rust is the most obvious, but it can be lead oxide on a battery post, which is "lead rust" instead of iron rust.
If your instrument indicates a minimum of resistance at a ground, it is testing the ground at a very low amperage. So, yes, a higher amperage test might indicate a complete failure instead of a limited failure that a low amperage test would show.
Bottom line. Just take the connection apart, scrape and clean the surfaces, and reassemble. Ditto with the battery grounds.