'(Only recently have you been able to buy one without a hard-to-find invitation).'
If by recently you mean 9 months ago then you're correct. I bought my Oneplus One in their web store in November 2014 without an invite. And I held it in my hands less then a week later.
'its only institutional shareholder is Chinese phone vendor Oppo Electronics'
Well, what I heard is that Oppo Electronis is NOT the maker of the Oppo phones, which would be Oppo Mobile: http://www.gizchina.com/2014/04/28/oneplus-responds-oppo-controversy/
So Oppo Mobile and Oneplus share an investor, but are not directly linked.