AWD car needs a new tire; Replace one or all 4

Went to Firestone today because I have a slow leak in one of my tires.
The car is a 2002 Subaru Impreza TS with factory spec tires 195/60/R15.
  Turns out the slow leak was due to a puncture in the sidewall of the
tire, so that tire is garbage.  The tires are all about a year old and
have decent meat on them, but the tech said you can't just replace one
tire on an AWD car, you have to replace all 4 as a set, because the new
one will be some sixteenths of an inch larger than all the rest.

Of course he'd say that :D

Now, I understand the concept and theory of this-  if all wheels are the
same circumference, they all rotate the same amount and internal
drivetrain components (center diff or viscous clutch) don't have to take
up the slack.  But... I have a hard time believing that an amount
measured in sixteenths of an inch is significant.  Surely a few pounds
of pressure off, or an unbalanced load (i.e., some fatass sitting in a
seat opposite some 80 pound child) would make just as much difference?

I declined to make any purchase at this time.  I know I'll need to
replace that one tire, but I have another vehicle to drive for now.  I
would like to replace the one tire only.  Replacing all 4 is a bit
unnecessary, right?

Thanks

-J