I had to read the Dick Act of 1903 32 stat. 775 (aka the Militia Act of 1903) for my master's degree program on military leadership. At no point does it limit Congress's ability to regulate civilian ownership of firearms. Who ever started this Internet rumor would have had better luck with the militia act of 1792 that required every able bodied man to keep and maintain a musket and 20 or so rounds of ammo. However, it was replaced by the Dick act that renamed the organized militia's in to the National Guard and made it a reserve force of the US Army, and required the secretary of War to pay for the Guard's weapons, equipment, and training.
I think who ever started this rumor chose an obscure statute at large that can not be easily found by looking it up the United State Code making it hard to prove or disprove.
Text of the militia act can be found here if you are so inclined.
The statutes at large of the United States of America, from December, 1901, to March, 1903, Volume 32, Part 1 chapter 196
http://books.google.com/books?id=ICU3AAAAIAAJ&pg=PA775(It's near the bottom and the top of the next page.)