I would do whatever you're engine manufacturer says to. Some may not warranty it if you don't. Some engines have cams broken in on a dyno, some don't. Some want you to baby the engine for a bit, some want you drive the living crap out of it.
Break in oil is a prudent thing. harm can be done if break in is not done correct. There is little harm in running break in oil twice, if the engine was already broken in . Id err on the side of running break in oil.