I've never heard of 'brown worms' and can only think it may be Lumbriculus variegatus (commonly called the California Black Worm). It is a segmented worm and looks redish-brownish in color. I did find a few references to the 'brown/black worm.'
As for getting a disease from them, not if they come from a good source and are kept PROPERLY. The sellers will tell you to keep them in the refrigerator, rinsing them with cool water daily to flush out those that have died. This is just to encourange you to keep buying them.
If you take a healthy batch of the worm and keep it in a CYLCED aquarium, they will reproduce and provide months (or if not overharvested) a perpetual food supply for your fish, provided you treat their tank as you would fish (water changes, feed them something healthy, etc).
If fed diseased worms (that have been kept in the refrigerator and are slowly dying day by day) or any other unhealthy food to your fish, then it will lower your fish's immune system. California black worms do not, however, 'carry' Mycobacterium marinum (fish tuberculosis or fish TB) from what I have read. If your fish DO have the disease, it CAN be transmitted to humans, but as a skin rash, and is easily cured in humans. Fish Tuberculosis is in no way related to Pulminary Tuberculosis (AKA consumption as it was once called) in humans. Treatment is not completly known to be effective in fish, but 5 days until death is not true. Some have had tank for years with it, but are careful not to add new fish to it, as those that survived are carriers.
I did read over the links you provided, but do not put much faith in what is said about feeding live foods. One says that bloodworms are mosquito larve which is not true (bloodworms are a larve of the midge fly).
