The 1-1/4 mile estimate is just about right.
Quite awhile back I used my GPS to actually measure the walks around various places at WDW. The link below will take you to the report about the walk around the Epcot area resorts.
From there you can link to the other walks if you'd like: MGM to Boardwalk, Boardwalk to Epcot, etc.
http://disboards.com/showthread.php?s=&threadid=130187
Obviously I don't have a direct report from BWV to MGM but a little math showed it around 1.25 miles.
From the BCV's to MGM, the <b>shortest</b> walk would probably be: Exit the villas but do not go through the BC itself, but instead take the walkway that goes past the outside of the BC rooms on the Epcot side. This will bring you out very close to the bridge that goes toward the Boardwalk. Follow the path to BWV, walk toward the main entrance but then turn right and go through the tunnel toward the Luna park pool. Go past the pool on the left, toward the canal, then follow the path by the canal all the way to MGM.
If you want to take the <b>longest</b> 'stroll' possible, then exit BCV's and go through the BC to get to the walkway by the boat dock. Turn right and follow the path to the Swan and Dolphin hotels (do not cross the bridge back toward the BW). After passing the hotels the path goes along the canal until it reaches Buena Vista Drive. There take the path up to street level, cross the bridge, then take the path down again to the other side of the canal. You're now on the Boardwalk side of the canal. From there follow the path under the bridge to MGM studios.
The in-between walk would be the one Rich outlined: Go through the BC to the walkway by the docks, turn right, follow around until it connects to the BW, then follow the path next to the canal up to MGM.