As was said, with more space than the thickness of a dollar bill, no problems.
The issue is not the barrel moving when you shoot. It is the barrel and wood heating at different rates if they are touching which causes problems. The slight enlargement of the steel during a string of shots could cause changing pressures from the wood, and it's the changing pressures which cause the groups to enlarge.
The goal of a proper fit of stock and steel is that everything be the same from shot to shot, other than temperature.
The typical deer hunter shoots once from a cold barrel. Bedding is hardly an issue. A prairie dog hunter shoots a smaller target, and lots of them in a relatively short time. Bedding is thus critical to success, with a warmed-up barrel.
For target shooters, it's even more critical, since a string of ten shots might be fired in a relatively short time--the barrel is even hotter at the end of the string.
Hope this helps as to the "why".
, Art