I believe it is an OSHA requirement that the rated capacity be shown on the hoist or bridge crane "assembly", but I don't believe I've ever seen it on the beam itself as an isolated element.

Agree with JHeight
Make them produce the specification.
Does not make any sense.

From OSHA regs in 29 CFR:
"1926.550(a)(2)
Rated load capacities, and recommended operating speeds, special hazard warnings, or instruction, shall be conspicuously posted on all equipment. Instructions or warnings shall be visible to the operator while he is at his control station."

"1926.550(d)
Overhead and gantry cranes.
1926.550(d)(1)
The rated load of the crane shall be plainly marked on each side of the crane, and if the crane has more than one hoisting unit, each hoist shall have its rated load marked on it or its load block, and this marking shall be clearly legible from the ground or floor."

From a few of the 90 results from an OSHA search of for 'crane capacity.'
http://www.osha-slc.gov/pls/oshaweb/owasrch.new_search_results?p_text=crane%20capacity&p_title=&in_clause='FULL_SITE','STANDARDS','INTERPRETATIONS','FEDERAL_REGISTER','SLTC_STATIC'&p_status=CURRENT&p_category=&p_logger=1

Overhead cranes used in general industry are governed by OSHA 29CFR1910.179 and the ASME B30 series of standards.

None of these standards require the support beams (runway beams) to be marked with a capacity rating.  OSHA 1910.179 requirements for capacity markings are the same as stated by 'kenvlach' above.

If the opinion of your 'inspecting body' was correct, then every industrial facility in the U.S. would be in violation!!

The only circumstance that I can imagine for that kind of requirement is in the case where you might have a portion of your runway system that is under-designed for the rated load of the crane.  On very rare occasion, I've seen this where the Owner installs a crane with higher capacity and maybe does some reinforcement to the runway structure in only one area of the building.  The Owner then marks the structure for the acceptable lifted loads in the various areas of the building.

Notwithstanding the above, I believe your 'inspecting body' is flat-out wrong.  If they've issued you any kind of report or other document, I would press them for a revision.

when you stamp a load capacity on a lifting beam, It is assumed that the entire support structure can hold that load.  If the support structure can not hold the load marked on the crane, the marked load should be changed.  I have never seen a code that requires the support structure to have a load capacity, however I think it is obvious that a crane should not have a stamped rating on it that is greater than what its support structure can hold.  

weron4u- if you consider the support structure part of the crane then yes its lifting capacity should be based on its weakest parts whether or not the bridge or boom of the crane can exceed that capacity.