I am following a site that is on the first position in the serps for a few competitive keywords. The strange thing is that more than 3000 people +1'd this site and that might be one of the reasons why it is doing so well.
I thought that only a few people were using Google+. The website is mainly visited by women and teenage girls. I would be surprised if so many would +1 the homepage. Or are they using some method which adds up all the +1's of the internal pages?
The site could be focusing on bringing their audience to Google+ (like for example if they're holding Hangouts that have become popular, or are specifically sharing unique content there). That's what I would do if I were specifically trying to build +1s.
Or they could buying +1s; you can probably get em cheap on fiverr.