Assuming you are soliciting opinions on this...

It seems to me that the answer to the question: "Which is more
important,
a thorough understanding of electronics or a great deal of
experience?"
depends upon the stated goal.

If the goal is to (eventually) be able to troubleshoot and repair
anything
that comes in the door, then I would cast my vote for technical
knowledge. For instance, in the case of the OP's problem, it would
seem to me that if poor solder joints on the tuner shielding are
really the problem, given a thorough understanding of how all the
circuitry works, one should be able to use a scope to examine
signals at various points and eventually ascertain that the tuner's
output is floating or whatever. (This is just an example, let's not
get into issues about whether or not one can probe into a tuner
and even see the actual signals.) So let's say for example it
took 2 hours of troubleshooting to find it.

OK, so now let's say that the goal is to be able to quickly and
profitably repair the majority of products customers are likely
to have - then it would seem that experience would be at least,
if not more, important. If I get 10 sets in a row like the OP's,
and I have a less thorough electronics background, it might
take me 3 or 4 hours to fix the first one. But I'll be able to
repair the next 9 in 1/2 hour.

OK, there's my two cents. If this was ridiculously obvious,
my apologies.