Prompted by these reports, VICE News tried to find the soldier shown on the picture and proving that the allegations were not correct, at least not in the sense as described by the New York Times:
On the diplomatic plane, allegations indicating direct involvement in the sense of Russian soldiers themselves being present were voiced by France during Security Council Meeting 7165 from 29 April 2014:
We are witnessing a a subversive operation that has been planned, barely disguised and orchestrated by Russia. Russian special forces do not even hide anymore. Some time ago, our Russian colleague denied their involvement in Crimea, while his President recognized it a few days later. No doubt, he will do the same with respect to current events in Ukraine. France strongly and unequivocally condemns those unacceptable attempts by Russia to destabilize Ukraine.
However, Russia has consistently denied at least direct involvement in the sense of sending its own troops to Ukraine at the same Security Meeting for instance (and throwing a verbal punch at the US and its large number of military bases abroad):
With regard to armed forces, our armed forces are on Russian territory. American forces are hardly at home. They are in Australia, Lithuania, Poland and on the Black Sea, where an American vessel has remained longer than it was invited to do. Yes, our troops do conduct training exercises. But they do so in a transparent manner and while upholding all existing international agreements. We do not have any aggressive intentions towards Ukraine. They Kyiv Government should keep a cool head and not engage in reckless activities with respect to the people in the south-east of the country, where there are many Russian citizens as well.
While Russia hasn’t changed its official position until fairly recently at least (see http://www.washingtonpost.com/world/putin-denies-russian-troops-are-in-ukraine-decrees-certain-deaths-secret/2015/05/28/9bb15092-0543-11e5-93f4-f24d4af7f97d_story.html), it seems to become harder to maintain every day. As a recent video by VICE News shows, everyone with a computer can determine that it seems very likely that Russian soldiers are present on Ukrainian territory. After all, they themselves, while not wearing official insignia, seem to have posted revealing pictures on Russian social network sites. Web 2.0 indeed does have some strange side effects.