Washed-out flash close-ups

As part of documenting her work, my wife takes photos of patients' skin.
In a dimly-lit room, she photographs the part of interest along with a
paper ruler and a slip of paper containing the particulars. For this task
she has been using a $90 Canon A-series P&S, using flash, in full auto
mode. The A-series was of particular convenience value because of the
ability to instantly replace dead AA batteries with fresh ones while
doing rounds.

Recently she asked if I had an old camera to spare, as she now has an
assistant and thus a need for a second camera. Jumping at the excuse to
upgrade something, I volunteered my trusty dusty Canon A710. I told her
it should do as well or better, and also used disposable batteries. Set
it for full automatic and matched the settings of the older P&S as best
I could.

A week or so later, she said "I still need a camera for work". When asked
what was wrong with the A710, she told me the paper ruler and tag were so
washed out that the text could not be read. So in her office I tried both
of them side by side, using my arm and a paper memo as test subjects. Sure
enough, using flash and full auto, the A710 could not properly expose
the skin AND the paper, where the el-cheapo did just fine.

I experimented with various metering modes (evaluative, spot, center-weighted)
but in flash mode this seems to make little difference. I tried dialing
down the exposure compensation a couple of stops, but then the skin was
too dark. Worse, she told me that she doesn't have time to fiddle with
settings, she wants to point and shoot, period, as she does with the
el-cheapo.

Why can the el-cheapo handle this situation but the better-equipped
model fails? I suspect the flash on the A710 is more powerful and, at
close range, simply produces too much light. Suggestions? I'm going to
try attenuating the flash by taping something over it as my next step.