OBR

May a BR overrun 1st base on a walk the same way he does on a ground ball and came back to the base?

I thought that this was legal (except in Fed) but a friend of mine says that the BR would be liable to be put out in this situation.

This has been argued to death on many occasions, but the consensus is:

OBR: It's ok
FED: You can be tagged out.

In OBR it's more than consensus - it's a published fact.

MLBUM 5.13 <i>NOTE: The batter-runner is not prohibited from overrunning first base on a base on balls (i.e.,
the batter-runner may overrun first base on a base on balls and is not in jeopardy of being put out
provided he returns immediately to first base). (See Official Baseball Rules 7.08(c)(EXCEPTION), 7.080), and 7.10(c).)</i>