Now, some of our august mechanic members are making noises like they
would be willing to sign their license # that the engine is
airworthy...

Actually, we were talking about the shop that did the annual providing
a new copy of the statement that on such and such a data... found
airworthy.

If, on the other hand, someone brought an engine into a shop, never
before seen, no logs... then yes, the AI has a bigger task on his
hands. First, the engine isn't airworthy without an annual inspection,
so he has to do that. I don't see (from that alone) any necessity to
do any more than the normal tests. No need (for just that) to tear
down the engine.

But then we hit the second snag. AD's. He also has to be able to sign
off that they are all complete and HOW they were performed. [We tend
to forget that second point.] Without logs, there is a good chance
that one of THOSE may require a teardown. And you are correct, the
cost of that may likely (depending upon engine and AD's) turn out to be
the cost of a full overhaul.

I think the problem many of us had with your original post was the use
of the word "CERTIFIED" instead of "airworthy." The engine is certified
if it has the correct data plate on it. I can find an old IO-360
rusting away in the back yard of a house I bought. Is it certified?
Sure, if the data plate is still attached. Is it airworthy? Almost
certainly not, neither from a legal nor mechanical standpoint.