I had to research a bit about Yandex in order to understand the implications there.
The story seems to be something like this:
[1] Yandex builds an app to crawl Facebook without Facebook's permission
[2] Facebook blocks Yandex
[3] Yandex gets licensed access to Facebook's firehose
[1] https://techcrunch.com/2013/01/11/yandex-wonder/
[2] http://www.reuters.com/article/net-us-yandex-facebook/yandex...
[3] https://techcrunch.com/2014/01/13/yandex-facebook/
There's certainly a plausible Kremlin long con here - fund Milner to invest in Facebook, ask Yandex to build a crawler for Facebook, expect that Facebook would shut it shut down, then suggest via Milner that there should be a partnership between Yandex and Facebook, thus gaining official access to Facebook's firehose, to be sent directly to Kremlin for analysis of message proliferation, and further influence of the American public.
The fundamental mistake there (the final move that allows you to be checkmated) is the firehose deal, not the investment.
In any case, thanks for making me think through the possible attack vector here. Your comment is the first one that was specific enough that made me think through why this could be a cause for concern.