On the SharePoint side of things, while I believe MS did oversell its capabilities, the problem was (could still be) that most places thought it was plug and play. It seriously wasn't. I don't know if things have gotten better but documentation those days was severely lacking. Add to that enterprises that were in the mindset that SharePoint was just another ASP .Net application and their in house devs could just pick it up without some sort of guidance.
There were a bunch of places where I was brought in to clean up the mess that happened because of those two things. I'm not sure if the landscape has changed or not but SharePoint is a beast unto itself and I've personally seen it implemented well at 30k+ seat organizations and the largest I've done was 50k seat org across 3 continents. It's not cheap to set up or customize but when it is done correctly, it does work.
Others just got it in a licensing transaction... they signed up for the Core CAL, and took care of their Windows, Exchange, SharePoint and SCCM licensing, even if they didn't use all of them. If you owned any two products (Exchange/SMS, Exchange/SharePoint), you actually saved money in the process.
I also see that the term "real BI" is a bit meaningless :).
In terms of the companies using it, it looks like I might be a bit off, but its probably somewhat dependent on the industry.
One company that I am following is http://www.domo.com/. The founder has a great blog (www.joshjames.com) and seems to be trying to shake up the BI space a bit. I would love to know their back office stack.
Then again, you really only want to do this if you already have SharePoint, since that's the web presence (it's a module in SharePoint called PerformancePoint). But SharePoint has sold a metric shitton of licenses (I don't know why). You're right to be hesitant to bring SharePoint in, but for those who have, it works all right. Even for "real BI" (whatever that means).
The backend stuff works well, and there are a lot of tools that can pick it up--my personal favorite being Tableau. Also, PowerView in Excel 2013 is pretty nifty, and it's what I've been waiting on since Microsoft acquired ProClarity in 2006.