I haven't seen the shirts you're talking about, but that type of feel could be discharge screen printing, water based screen printing or direct to garment printing.
Most likely the company gets the garments custom made by overseas factories (china, india, mexico, honduras, etc) and the garments may not be readily available for wholesale purchase.
You could try tracking down the manufacturer by looking at the RN number in the label and finding the company name, although that may or may not lead to a correct source (it might just lead you to the Express company).