No, specialized facilities means some kind of facility that is only available in your work location in Nebraska that the employer could not procure in NY. The example on the bulletin @VanessaA provided is a test race track in a state different than NY because it is not available near the employer in New York.
If you telecommute for a New York company, due to their convenience of the employer rule, it is very likely to be taxed by New York. It is only if they assign you to a different region for some specialized purpose that you would not be subject to NY tax. If you could be doing your job from anywhere, then they treat you as an in-house employee and subject to NY taxes.
