It very well could be the water pump. I never knew it was recommended to change that when changing the timing belt.
The reason it's recommended is because
1) it's a decent interval for replacing it, and
2) it's a significant amount of labor to change the timing belt, and it's only another 10 minutes worth of work to replace the water pump while you're in there.
I just did my timing belt and water pump, and here were the steps (I forgot some the first time through, hence the negative numbers):
-2) drain coolant, disconnect battery
-1) remove hood (it makes everything else so much easier)
0) remove windshield washer tank (it makes everything else so much easier)
1) remove alternator and belt
2) remove cruise control and wiring harness that passes over the valve cover
3) remove idler pulley and A/C compressor belt
4) remove power steering belt
5) remove power steering pump bracket
6) remove valve cover
7) remove upper timing belt cover
8) remove bolts from water pump pulley
9) remove middle timing belt cover
10) remove crankshaft pulley bolt, pulley, timing belt guide, and lower timing belt cover
11) loosen timing belt tensioner
12) remove passenger side engine mount
13) remove timing belt
14) remove water pumpSteps -2 through 13 are all prerequisites to removing the water pump