The instruction you refer to isn't specific to Boots but applies to all rubber hot water bottles. Domestic hot water cylinders are usually made of copper and small particles of copper get into the water supply which is why we should never drink from the hot tap. In the same way, copper causes damage to rubber and over time may shorten the life of your hot water bottle.
I have to honest and say this is a rule I disregard as "hot tap temperature" is just right for me. I believe that using water that is too hot is not only more dangerous, but likely to cause greater damage to the bottle than hot tap water.. I still manage to get many years use out of my bottles.
Incidently, as far as your old bottle is concerned, (assuming you still have it) I wouldn't throw it out just because a few bits of rubber came out while being emptied. This happens as bottles gets older, but is only the early stages of wear. I find that mine still have many months of safe use left in them at this stage. It's only when cracks start to appear in the rubber that I would think about replacing them.