You’re correct if you do not keep your bird feeders clean. If you keep your feeders cleaned properly, they will not spread disease. I’m an amateur birder, and of course a nurse, so I was concerned as well about that (and not just my hummingbird feeders, but my other seed/suet feeders as well). I’m an Audubon Society member, so I reached out to them, as as to the Cornell Lab of Ornithology to find out how to properly maintain all my feeders. I only fill my hummingbird feeders 1/2 way, empty out the water frequently about every 3 to 5 days (more frequently in the summer, every 2-3 days), . Keep my feeders in the shade, and I clean them all out with soap and water and a brush, then soak them in a 1:9 bleach to water solution in a bucket fully immersed for at least 3 minutes. I dry the seed feeders before I fill them with seed or suet, and I rinse my hummingbird feeders really well prior to refilling them. So, if you’re good about cleaning them, they will not transmit diseases. Also, you need to keep your fountains and bird baths cleaned as well. I scrub mine out once a week, and pour a little bleach in them, then cover them for a a day to let the bleach dissipate before I let the birds back to bathe or drink.
http://marin.wbu.com/content/show/96477
http://www.seaandsageaudubon.org/Conservation/TreeTrimming/HummerFeederCare.html