Someone correct me if I'm wrong (it's been a few years), but I believe cross-rolling is an attempt to avoid the directional variation of mechanical properties that you get with rolled plate. That is, the tensile strength of a test sample cut parallel to the rolling direction is significantly different than the strength of a sample cut from the same plate but perpendicular to the rolling direction.
There's nothing in the ASME spec to my knowledge that prohibits this fabrication practice. As long as it meets the chemistry, mechanical, microstructural and finish requirements of the spec, how it gets there is not specified.