Share 'Putting smaller tires on a Hybrid Bike'

Last summer I purchased a Specialized Sirrus Hybrid bike. There are currently 700x32c tires on the bike. Someone had recommended that I would notice a significant difference if swapped the original tires out for 700x28c tires, and still be able to keep my current rims. I was told that if I went down to as far as 700x25c tires, I would be "pushing it," and would have to purchase new rims as well.…