Something similar happened to me. I was a citizen of Uzbekistan at the time. I was about to fly out of Almaty. When the lady at the checkpoint saw my passport, she asked where my exit visa was. I never knew all the Uzbek citizens needed one to leave the post Soviet territory. So, I was denied my seat on the plane. Had to renew my ticket for $50. Come next day, another lady at the checkpoint says the same thing - without the exit visa I am not going anywhere. The plane was already boarding and I was about to miss it again. She saw me getting agitated and says "why don't you talk to this man here?". He said everything could be arranged for mere $300. Even though I was an actual student and poor as a church mouse, I had to pay it. I was let out.
Curious why you found out you needed an exit visa, rebooked, and came back without one. Were you just hoping you'd get lucky with the border staff the second time?
I must say this is strange. As an Uzbek citizen you don't need an exit visa (OVIR) to go to Kazakhstan or Russia. I guess they were trying to hustle you.
@pavel_lishin: The exit visa costs about $50 -- you pay a fee to the government and possibly a fee to fill out the application. These days it takes anywhere between 2 weeks to 2 months to get it. Depending on the country you want to visit or where you have been previously (based on your application), you might also have to go through a security interview with intelligence officers.