Think I know what David means....SOME light, stress relieved barrels don't walk;some do.
I know Dober had a bitch of a time with a light contour custom which is very popular and has an excellent reputation for accuracy. They are stress relieved far as I know.I won't say the name of the maker....no point in it.
I've had very good luck with light contours in 270/7mm made by Kreiger and Douglas. Both are stress relieved pretty extensively at various points of manufacture.
I expected great results from the Kreigers;have to admit the Douglas tubes I've had caught me off guard...better than expected.