Unless a licensed professional engineer, checked the design, provided the calculations, details and specifications, I would question every bit of what a steel supplier says. For anyone considering the design and construction of an overhead lifting device, it has to be engineered. I realize that AISC and similar reference material may provide load tables and beam sizes, but there is missing information, which cannot be arbitrarily decided based on looks or opinion, footings, piers, columns, rigging, safety margin, all have to be designed, coordinated, checked out etc. to insure that it will safely handle the loading imposed on it, and will in fact have a safety factor.
One of the reasons I think its just a necessity is that years later, someone else may have access to what a person has previously built and will not have any details on it safe working limits, a device like this after being properly designed should also be labled stating the safe working capacity.
I say this having been in the commercial building construction industry, no steel supplier I have ever dealt with would size anything, its engineered on the building design documents, which are then used for bidding purposes, steel supplier will then after being awarded a contract, will detail shop drawings for the steel they will provide, and those shop drawings have to be approved, approved as note by the engineer of record, whom will check those drawings against the structural drawings he provided for the job.
Its's like residential housing, most carpenters or framers have a working knowledge of materials and can say what you will need say for example a roof framing job, 2x..... so many inches on center, etc. and it will work, you just can't do that with steel, given the loading and forces at work and one should never really do that in general, any structure or lifting device needs to be engineered to be safe, which means its designed for a specific purpose, with parameters of use and load limits, all components included, not just a beam that was sized as per what someone says will work, unless that person did or had someone do the necessary engineering, which to be honest, would not take long for an experienced engineer to provide.
Only reason I post this is to make sure someone does not get it in their head that steel suppliers are designers, they are not, and its highly likely no information would be typically provided given the liability it presents to the supplier, unless they have design capability and have errors and omissions insurance.