Bar stock is only deformed in one (long ways) direction. Forgings produce parts in near net shape. If a bar is very close to what your end product is, then perhaps bar stock is good enough, but if your shape is a tee or elbow, then it isn't. This is (or should be, haven't read it) pretty clearly spelled out in the ASTM specification (big hint here: buy a copy, it's not that expensive). Forgings get deformed in two directions, sometimes three if upset forged. Bar stock can/will have longitudinal-direction defects, which may or may not open up under pressure or after some number of cycles of loading. Since fittings per the spec. are not intended to be hydro-tested, a machined bar stock fitting is a risk, one that your customer has not elected to take.
Redpicker has it right with "I would assume the concern is, for some types of fittings such as elbows or tees, the forging process will direct the grain flow more in line with the direction of principal loading stress and that with a fitting machined from bar stock, you would not get this preferential grain flow."
You could always call and ask your customer for an exception to the spec.