The given function is equivalent to !b | a & b & c and as you wrote, also equivalent to !b | a & c which is a minimal DNF. Note that the text above does not state that !b | a & c is a minimal DNF, it just says that the formula can be shrinked down (minimized/reduced) to that.

The minimal DNF is however not useful, since we want a DNF whose cubes are non-overlapping, i.e., do not share common minterms, since if we have a DNF with non-overlapping cubes, we can replace the disjunction with an exclusive disjunction as explained in the text. You cannot do the same for !b | a & c since these cubes share the minterm a&!b&c.