Thanks to check this report. andyour blend file actually worked, but it was different how set-up material, in outliner.
your attached blend file, "mat_blue" link material for "object" but at same time "mat blue" still keep link with "data" of cube1

this is my download blend.

But I report when I remove link material for "data". only link with "object"
(just change link type to object, I feel blender keep material link of "data". but I clean up it. sorry I miss discribe it)

please test with this blend, it only remove link of mat_blue with "data" but keep link with "object" which you offered blned file.
after remove link for "data", cube1 can not transfer material any more.
(but material link with object, then the cube1 can show mat_blue)

Sorry, didnt notice the Material was still linked with data.

So yes, the Copy Material to Others operator only works with materials on object data (checked relevant code)

An alternative to using above operator is using the Make Links > Materials operator.
Afaics this operator has a couple of advantages:

• will work with materialslots linked to objects (not objectdata)
• will respect this user preference

couple of issues/notes with 'Copy Material to Others':

• actually copies all materials (should be plural -- tooltip already says so)
• wont work with materialslots linked to objects (not objectdata)
• code history implies this was added as a (workaround?) in 2.5 in October 2009 when Make Links wasnt available, but then Make Links actually came back in November 2009

I might be missing something here, but it seems to me that (given the fact those two ops do very similar things - and one of them actually seems 'superior') we could replace Copy Material to Others with Make Links > Materials?

I'd be happy to do the patch, but kindly asking @Campbell Barton (campbellbarton) for his opinion/advice here...

Thanks advices. I could understand, Link material have many advantage, and plan to use it more.
but I may need to test it, to confrim it can be substitute of my current plan.

Because I hope to make "skin set exchanger" or "full mat exchange tool" , which can save current "all slot materials" of complex mesh as one "skin set" in another blend.file (skin_sets.blend) .
Skin_sets.blend need to store many material sets with each mesh (I plan to use duplicated link mesh) which named as each skin sets.

Then I hoped to use material which " link with object." because, "link duplicated mesh" can keep individual "skin sets". it may make blend file size small.

when I overwrite skin of current working mesh, I planed to append mesh(named as " skinset1" etc) , and copy and paste all materials. then I remove donner mesh from working scene. I planed to auto-mate these process as python add-on just for my purpose.

So if Link material work for my plan, I may need not use "copy and paste material", but as you said, actually these 2 tool seems a little different. Then I need to test it more. I think, (I am not beteran user), I may better not judge to remove old tool. if it still need for each user purpose )
and thanks test my report, and teach me about "link material" . I try it.

And,,, I really hope, if blender offer add-on, which I dsicribed above.. I know, I can easy keep material, and make material lbirary, there are already add-on for these purpose. but blender have not offered, tool or add on, which can save all material slots materials, as skin-set, and re apply it . so if you feel it seems useful, hope
you request it with clear words.
(I requested it in right-clcik select, but I could not get good response,,,)

please dont claim the task youself, this will most likely prevent others from looking at it

Will fix, having 100% proper fullproof solution is likely impossible given the weird mixed object/obdata relations with materials, but should usually give expected results...