It is quite possible for soldiers to cross a frontier ''by accident on an unmarked section'', and that is how Moscow explains the capture of a group of Russian paratroopers on Ukrainian territory last weekend. Poor lambs, they just wandered across the border by mistake.
The flaw in this story is that the 10 captured Russian soldiers, from the 331st Regiment of the 98th Guards Airborne Division, were caught in a group of unmarked vehicles 20km inside Ukraine.
That's a third of the way from the Russian border to the besieged rebel city of Donetsk, and it's really hard to explain away as a navigational error.
Besides, there is plenty of other evidence (though no other video interviews with captured Russian troops) to show that there is now a three-pronged Russian offensive under way in eastern Ukraine.
There are probably fewer than a thousand Russian regular army troops on Ukrainian territory at the moment, but their purpose is clearly to stop the collapse of the pro-Russian rebels and reverse the momentum in the ground war.
Last week, the Ukrainian forces finally cut the last remaining road from Russia to the besieged city of Luhansk, shortly after a large convoy of Russian trucks violated Ukrainian sovereignty and drove up that road to deliver ''humanitarian'' aid to the city.
The rebel forces have now launched a counteroffensive to reopen the road, and Russian self-propelled artillery units have entered Ukraine in the Krasnodon area to support their attacks.
Another Russian force, including tanks, crossed the border on August 24, 50km south of Donetsk, the capital of the other rebel province, and is trying to open a corridor to that city. (The captured paratroopers were part of that force, which is currently stalled near Ilovaisk.)
And on August 25 a column of Russian armour crossed into Ukraine well to the south, heading west along the coast of the Sea of Azov towards the port city of Mariupol.
This last incursion, presumably an attempt to open a third front and relieve the pressure on the two besieged cities, is now stopped at Novoazovsk, about 30km east of Mariupol.
The Ukrainian forces say they destroyed a dozen armoured infantry carriers there. Russian helicopter gunships also killed four Ukrainian border guards and wounded three others in an attack on a border post east of Luhansk on Tuesday.
It's not yet all-out war between Russia and Ukraine, but there is no doubt that Ukrainian forces are now in direct combat with Russian troops on several fronts. Russia still officially denies all this, of course, but its denials are not meant to be believed.
Rather than see the separatist forces that Moscow has sponsored in the two eastern Ukrainian provinces simply collapse, Russian President Vladimir Putin has decided to escalate the conflict.
The message is that Russia will do whatever is necessary militarily to keep the rebellion alive.
But is that really true?
Mr Putin is now just one step short of a full Russian invasion of eastern Ukraine, and Russia is already suffering serious economic sanctions.
Take that last step, and it's back to the Cold War - a war that Russia would ultimately lose, and it wouldn't take 40 years this time, either.
Today's Russia has only half the population of the old Soviet Union, and it is no longer a major industrial power.
Without its oil and gas exports, its citizens would be as poor as Ukrainians. If Nato started to take the ''Russian threat'' really seriously and rearmed itself accordingly, Russia simply couldn't keep up militarily - and even trying would wreck its fragile economy. In the end, that would probably bring Mr Putin down.
He presumably understands this at some level, but his pride, and his desire to restore Russian power, won't let him just accept defeat.
So the current escalation is best seen as his next move in a game of chicken: can he frighten the West into making a deal that saves his face and turns Ukraine back into a political and economic dependency of Russia?
The answer is: probably not.
Ukraine's president, Petro Poroshenko, certainly does not intend to go back to the old days.
When he called a parliamentary election last week, he was effectively declaring that Ukraine will continue to be a sovereign and centralised state, not the neutered and decentralised state that Moscow wants, and that it will keep its options open on joining the European Union and even Nato.
The problem with games of chicken is that each player must demonstrate his willingness to go all the way, even though going all the way is crazy.
The first one to give way to an attack of sanity loses.
The only way to avoid a disastrous smash-up and still not lose is for both players to go sane at exactly the same time. That is what diplomacy is for, but so far it isn't working.
- Gwynne Dyer is an independent London journalist.
