I feel like honesty isn't Putin's biggest concern. His country is. I'm sure everything he does is so he can be in control. He's a dictator so if he wants to lie about something who is going to stop him? It's already been proven that he's a killer to those who cross him so who will contradict what he has to say?
Yes, I feel that Russia is the type of nation that acts in a shame-based manner. Instead of openly admitting that many of its citizens are infected with the HIV virus, they will probably try to cover it up. They want to look good in the world stage. That's more important to them than helping their own people.
If there's a government source putting out a statistic, you can be sure that there's some sort of agenda behind that statistic. In America, we drop people off the employment rolls just so we can pretend that unemployment is going down. I'm positive that the same things happen in Russia to make the government look better.
No, I do not think that the Russian government is minimizing the number of persons infected with the HIV virus. I think the Russian government only cares about the people in power. They might make it seem like they are helping, but they simply want to be the most powerful country.