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PC Users have to keep their Origin up to date to avoid issues so I can imagine they have tried to do something similar. I didn't think the Mac patch was available yet. If you download Origin and it doesn't help then no harm done and you can get rid of Origin on the computer easily enough. As for the patch, a lot of people are having issues with it not just Mac users. Origin isn't a horrible program. It's no worse than using Steam or Skype. You don't have to leave it up at all. You can choose to never have it on.
The best people to ask since Mac Origin is still so new would be EA customer service or to try it yourself. If downloading Origin helps you with the patch, then you know it's probably just the nature of the beast unfortunately.