Pretty sure they did use their own picks.. The 2 years prior to drafting James Harden, they won 20 and 23 games. Ibaka may have been via trade but Durant, Westbrook, and Harden were all high draft picks they got due to sheer sucktitude, and to their credit, they didn't miss on any of those picks
Got curious and looked it up. Can't see which picks were theirs and which picks they traded for, but Presti or somebody on his staff has a hell of an eye for talent. Presti took over in June of 2007.
In 2007, OKC (or Seattle I guess) drafted Kevin Durant with the second pick (basically a no brainer) but picked up Carl Landry and Glen Davis with the 31st and 35th overall picks. I would say both have greatly exceeded the average career for second round picks.
In 2008, They took Westbrook 4th and Ibaka 24th. Again, you expect to his with the 4th, but Ibaka was a damn good pick at 24th. They did take Walter Sharpe with the 32nd pick which obviously didn't work out, but I think that was a decent flyer to take. Walter Sharpe had the potential to be a good NBA player if he got his head straight, and that's not a terrible way to use a second round pick. They also had three last second round picks that basically amounted to nothing.
In 2009, they drafted Harden 3rd and Rodrique Beabois 25th. I don' think Harden was an obvious pick at 3rd and I guess Rodrique Beabois was his first true miss in the draft unless I have just missed him doing something.
That's a damn good three year stretch. So looks like my initial statement was completely wrong. You need maybe a little bit of luck to have a true franchise player available when you have a high draft pick, but it's probably more important that you hit on your draft picks. Getting Ibaka, Carl Landry, and Glen Davis with the 24th, 31st, and 35th picks gives you a lot of valuable assets from picks that are generally not that valuable.