Keep in mind that some (I would say most) companies use recycled steel - so it may not be possible to trace the origins of the content. So they may use the "...with global materials" disclaimer just to cover their bases. The steel may be recycled, cast, forged, heat treated and tested in America, which I think still counts for something. As long as the steel meets specs, it's good. Also keep in mind that there are thousands of grades of steel, intended for various purposes.
Low quality tools from China may be made of poor steel (assuming it actually is steel and not aluminum or some other metal) with lots of impurities, or may not be properly treated at all. They are probably not as careful about the materials they source whether it's "virgin" or recycled. The latter of which could have anything in it, including lead or other toxic materials. A more reputable company may do QC and materials checking, but all of the endless Ebay/Amazon sellers with nonsensical "brand" names are very likely not doing so. Keep that in mind when shopping.
Companies that make a point to use all US steel are fine, but the actual manufacturing and finishing processes are probably more important.