Here's an interesting story in the International Herald Times about Putin's complaints over recent US legislation increasing national security oversite over foreign investments in the US. It's interesting from a few perspectives.
First, Russia has shown that it can't be trusted with regard to foreign investment in Russia:
In recent months, foreign oil companies have been forced to cede control of a number of major projects which they acquired in the 1990s, most notably with the sale by Royal Dutch Shell of a controlling stake in the Sakhalin-2 project, and BP's sale of its stake in the Kovykta gas field.
The Russian state-run natural gas monopoly Gazprom was the buyer of both.
Second, and on a related note, I have to agree with limitations on purchases of American businesses by foreign state-owned companies. I have less concern about purchases by purely private entities in nations that recognize property rights.
Regarding the general concept of government limits on foreign investment, I'm a bit more undecided. On the one hand, there certainly can be national security interests, be it regarding infrastructure (such as energy companies) and high technology. It likely makes sense for such investments to be vetted.
But ultimately, that Putin would make such a complaint is a bit hypocritcal. As a wannabe dictator, Putin has very little room to talk.