I didn't have to travel for the Olympics in 2010, but event tickets were done by lottery. No idea about the hospitality aspect.
One thing to note for 2010 was that Visa was a marquee sponsor, so tickets could only be purchased using Visa credit cards. If you only had Mastercard, then you wouldn't have been able to get tickets.
I ended up getting tickets to Czechia/Slovakia and Finald/Belarus round robin hockey games. Based on where I got picked in the lottery, all Canada, USA, and medal round tickets were long gone.
We went to some other events, too, but the best part of the Olympic experience for me was going to the country houses and watching events on big screens where those countries were medal hopefuls... like going to the Dutch House and watching speed skating. So even if you can't get to live events that you wanted, make sure you pop into the country houses for a fun experience.