OK, you've got me out of lurk mode.

I think in either case the person should eat the time. I write software for
a living and this happens all the time.  I never charge a client for hours
spent just trying to diagnoses a problem that I cannot fix. What I'll
usually do is spend a certain amount of time on something then tell them
that either I can start billing forward while I scratch my head, ignore the
problem or find someone else to fix it.  99% of the time they choose the
first option but I let them know in advance that I'll be charging for head
scratching.  With some of my clients I tell them unless a problem is 100%
reproducible I will not even look at it.

I believe this comes with the territory. People think I'm getting rich off
my hourly rate but that rate is there to cushion against all the time I eat
plus all the hardware, software, health insurance, etc. etc.

What I do is not much different from what mechanics do. Someone telling me a
web service is timing out allot around 3 PM is the same as saying my car
makes a thumping noise after I drive it for about an hour in the rain when
it's less than 45 degrees outside.  I also have to deal with "liars" all the
time who say they did not press a certain button when I know that they did.

Bryan