Ooh! Simple question, complicated answer. Short answer is "no." He didn't.
Thing is, Chekhov doesn't want to just...let them go. He'd never be able to go and buy a candy bar in peace again. :P
On the other hand, the Ukrainian judicial system and the jails had (and still have, to a lesser degree, sadly) some real problems. Overcrowding, tuberculosis (nope, not just for cheesy Victorian romance novels, it's still A Thing in some parts of the world), unsanitary conditions, overly long waits for trials, sometimes even active abuse to get confessions, etc. (To be clear, things are better now in basically every area of basic rights than it was in the mid-1990s but that's a really complicated discussion so sorry to cut it short.)
The Ukrainian constitution (which has pretty decent laws about these things) wasn't ratified until 1996, and still isn't always followed. Growing a democracy's political culture is like growing a tree -- it's a gradual process. (It might not have been passed in the comic timeline. Instability and stuff.)
Thing is, in this alternate timeline, there's a war...ish...thing. And human rights often suffer in (quasi)wartime, even in really democratic countries.
So Chekhov knows these guys will probably have it pretty bad if they admit that they're Bodhan's assassins. Odds are they won't get a trial for an indefinite period, be held in bad conditions, maybe even be tortured. (Don't forget that the USSR was only six-odd years before and basically the same people are in power...) They also both have injuries that need treatment.
And Chekhov doesn't want Bohdan to have Heroic Ukrainian Martyrs who Fought Valiantly Against the Russian Interloper. It's in Chekhov's political interests to to have these kids ID'd as simple muggers, get a "speedy trial" (like we call it where I come from), not Suffer Heroically For The Noble Cause, and have just a boring and unfun time in jail as opposed to a horrific one. It's also in the interests of the people who just...tried to kill him.
That's the thing about Chekhov...it's sometimes hard for strangers to know if he's saving their necks for some complicated Machiavellian political reasons, or if he's just a decent man.
Thanks for the question, sorry about the answer! :)