Does not sound like a rod knock. Sounds like your standard valve train chatter. Can you record a video of the noise when you rev up the engine.
A lot of people are not familiar the type of shims required to adjust the lash on these engines. I’ve dealt with plenty of 3vzes that have been “repaired incorrectly”.
When I bought my 4Runner it always had a valve train tick and lacked power. When I rebuilt it and went through the cylinder heads, the lash was wayyyyyy off. I was surprised it could even run with the amount of lash it had.
Ask him how he adjusted the valve lash.

Also to determine a burnt valve you can perform a cylinder head leak down test. If you are unfamiliar with this. YouTube it and you’ll find a break down of what to do and how to verify a burnt valve concern.