I have no idea about the merits of the cases but there certainly have been recent reports of "questionable" arrests and convictions of Russian businessmen and billionaires in the media ["A court convicted Mr. Navalny on what were widely seen as trumped-up charges"]: August 28, 2013 "Political Endurance Test for Russian Billionaire"
I don't know whether businessmen reach prominence because of illegal business activities, whether politically unpopular stands are the cause of their difficulties, or whether successful businesses are just too tempting for the state to leave in private hands. Understanding these issues is essential before investing significant amounts of money for the "long run".
Obviously there are reports in the American media of businessmen being arrested in the United States as well (many of these cases sound justified to me). Perhaps Russian readers are concerned by those reports. I'll defer to a subject matter expert to determine the legitimacy of the Russian businessmen arrests and the legal stability of ventures and investments in Russia.
I did some consulting with HP about 15 years ago, when Russia was in the Glasnost era. My contacts in HP told me that they had been very interested in Russia but were pulling out because of changes in government policies (they were making major investments in China). Nothing more specific than that, but I got the feeling that they had no trust in Putin. Any time a country is run by a central figure like that you run the dual risk of him arbitrarily changing the rules or dying and leaving behind a power vacuum.
In my opinion,if Russia follows the example of China where the private entrpreneurs have a free hand in developing their business while the governemnet concentrates on the policies of Nationa Interest and security, then it can be a very good opportunity for global investors.
The capabilities and creativity of Russian scientists and engineers are well known. Corporations seeking to invest in Russia, however, have to ask a key question: what assurances are there of contract permanence, security, and the rule of law? Too often successful businesses in Russia encounter interference from organized crime or government interventions. If corporations are to make long term investments, they need to be confident that the playing field will remain level.