Of course he is lying, and he was lying all the time. What did you expect all the time? Lying is part of the strategy, and the strategy is to influence Western public opinion - by conditioning it.
You have to give it to him, he is playing it very clever. Many smoke screens, from claims about troop incursions, rumours about volunteers, little green men, to convoys with mysterious white trucks. Every time there is a healdine. And every time the awareness of the public takes slightly more easily note of it, is more used to it, and slightly less interested.
As a former psychologist I can nothing but aplaude the psychological cleverness of this operation.

That is old fashoned KGB destabilizing methods - and obviously it is extremely effective. The KGB knew why they rated the impact of psychological ops more important than any other major intelligence agency, maybe with the exception of the CIA, and I think in the old days even the CIA could learn some tricks from it.
What the Russians are now doing is establishing a land corridor to the Crimean, which they desperately need over the next years before any alternative logistical supply routes over to-be-build streets and bridges or ferry lines could be completed. Also, the goal may be to establish supply lines via reliably controlled land corridors to Moldavia/Transnistria.
I cannot help it, but how Putin succeedes in making Western oh so clever politicians look like stupid schoolboys and chases them around to his liking, makes me grinning over the event taken for itself. I am sure he read Machiavelli carefully. The cause can be debated, but the execution, even where it took improvisations, is really nice.
As I said, old-fashioned KGB operations school.
What should Europe do? NOT intervening in the Ukraine, not sendign forces, not sending military goods. The Ukraine is a failed political experiment, and an infinite black hole to throw oney into that we do not really have (all nations de facto live in a status of delayed filing of insolvency). The Ukraine has nothing that is of interest for us, is just another wide open mouth that wants to get fed like there already are so many others in the EU. But NATO should massively beef up the defence capacities in NATO's Eastern borderstates. And by that I do not mean any acts meant as political signals only, but very robust and solid military measures. That would break several treaties of NATO with Russia over the East-enlargement of NATO in the last decade and the demilitarised areas there that Russia was promised, but NATO has not been shy to break other promises to the Russians before, and the current crisis shows that the rules of the game have changed anyway, and irreversibly. Sticking unilaterally to the old rules, means to take huge risks. While reinforcing NATO capacities in the East, also takes risks.
Welcome to the end of the policy of détente. Live with it. Or get chased around by Russia next time - once again.