One thing to check is whether the problem machine is running a 64-bit or 32-bit version of Office. I do not mean the computer itself (your AddIn can happily support a combination of 32-bit and 64-bit machines), I mean Office software.
We were stuck as you tried to understand why our admin worked on some machines and not on others, and in the end it turned out that the problem with 32-bit versions of 64-bit versions of Office turned out to be a problem in itself.
The solution was to force all users to use the same 32-bit version of Office.
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