It is generally legal for an employer to require employees to come to work when they are not scheduled to do so. Please look at my Avvo guide to at-will employment which may help you understand employment rights in a non-union setting: http://www.avvo.com/legal-guides/ugc/an-overview-of-at-will-employment-all-states.
The legality of the employer's "captive audience" meeting depends on many factors, some of which are what statements it made during that meeting, whether statements were presented as facts or opinion, whether there were threats or coercive comments, the timing of the meeting, the duration of the meeting, and more.
You may wish to contact the union organizers in private and let them know what happened. Provide as much info as you can regarding the specific statements made. Most unions that engage in organizing drives understand that employers may hold captive audience meetings, and the union organizing your workplace is most likely clued in to this kind of thing.
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Your employer can call a meeting during work hours to present its anti-union message although there are some things the employer cannot say. You should talk to the union organizers about what happened and what was said.
Generally speaking, yes, this is fine. Union representatives will be able to tell you if the hospital has agreed to some other rule on that matter but be careful not to let either side get you too fired up.