Drive belt replaced then immediately head gasket leaked

During routine maintenance my Toyota dealer noticed the drive belt was worn and suggested replacement. Although too pricey for the job, we agreed, and it was replaced. The next day we left town. Two weeks later we returned, and I drove the car twice. The first time the car was normal. The second time it sounded rough, which in 18 years of life it has never done. The car has been maintained scrupulously. I immediately took it to the dealer, and they ran the codes and said cylinder one has signs of coolant, so I need the head gasket replaced for $4,500.00.

[A local shop will not do it because the car is old and will replace the engine. I am attached to this engine, which is silly, but it has never shown signs of wear and my old Toyota ran over 300,000 miles. I am not eager to go this route without proof that the leak indicates stripped head bolt holes or something with cascading consequences like that].

I think $4,500.00 is too much money and I am seeking other options; but my question is whether the tension on the fan belt being wrong, or something else about that service when the belt was replaced could have affected the water pump and thus the head gasket. I did not see a red light or temperature warning come on. After the engine ran rough for a few minutes and then smoothed out, consistent with the coolant burning off, the Check Engine light came on and that is when I took the car in and got the head gasket diagnosis. Thus, the car ran maybe 10 miles with the Check Engine sign before it was delivered back to the dealer.

Of course, the dealer would be loath to suggest or admit a connection between the belt replacement and the leak, but the closeness in time is rather suggestive. Can this be possible?

Thanks,
Cynthia and Rich
San Diego