The outer barrel is the "gun barrel" of your M4, the outside part that you see (which would be the barrel of a real M4), versus the slim brass barrel that actually shoots the BBs (which is hidden inside the outer barrel).
I don't know how the stock ECHO barrel is built, it it's like the TM outer barrels it's actually not just one piece, and not all that solid all by itself. Reinforced outer barrels usually meant one piece outer barrels that could be used on TM guns, which made everything up front more solid.
If the ECHO barrel is one piece, it could be that it's made from a cheap pot metal which can't really support much stress, and would break from the weight of the M203.
I'm not really sure what you mean by people not liking outer barrels.
As for reinforcing yourself... got a machine shop?