Interesting point. I hadn't really distinguished between audits done by different parties, & I'm not sure that I would. The question was really to anyone doing an audit, 1st, 2nd or 3rd.
I know that I & clients appreciate an audit report (eg, from a 3rd party audit) if it's apparently fair and balanced (ie, gives credit where it's due, as well as observing nonconformity/weakness), rather than if it solely focusses on what's wrong. Tthe thinking may go something like 'hmm, the auditor's seen that we do this or this well, or have improved that, so over there when they say we need to improve, we should take notice of that & consider what they say carefully".
I'm not of course suggesting anyone ignores audit reports that are solely negative, but even-handed reporting (assuming always it is justified) is usually better received.