NO got incredibly lucky getting the #1 pick. They very well could (should?) have ended up with the #4 pick.
Additionally, they still could potentially lose Eric Gordon to free agency. Had they not gotten the #1, I bet the odds of Gordon leaving would have increased.
So, in an alternate universe, the Hornets could have ended up with a top-10 pick for Chris Paul, instead of whatever the package from Houston could have gotten them. Let's not pretend that the Hornets couldn't have flipped those assets at a later time.
On your first point: A team of Odom, Scola and Martin would have obviously been a "better" team than the one they fielded for a season, but not long term. Let's just assume that team would have won as many games as the Rockets... who almost made the playoffs, but got stuck with the 14th pick. Perpetual mediocrity. Trading Chris Paul for young talent and draft picks was essentially a way to go into "tank mode" (which I fully support under these circumstances) and the team more than likely was going to end up with a top 5 pick to go with the #10 timberwolves pick they got from the Clippers. Just smarter all-around. Landing the top pick was a best-case scenario, but even without Anthony Davis, it was a better deal... anything to prevent submarining the franchise with albatross contracts and perpetual mediocrity. They gave themselves a chance at a superstar and that's all you really can do.
On your second point... Eric Gordon is a restricted free agent. They were never going to "lose him". They just match any offer. No team is stupid enough to trade for a fringe 23 year old allstar and then let him walk for nothing, because it "costs too much". The worst-case scenario with Gordon was, is and will always be that he refuses to sign long-term and just takes a 1 year qualifying offer for 2012-13... in which case the HOrnets retain him as an asset and have an entire season to figure out what to do with him.
On your third point... that alternate universe doesn't exist. They would have had their own pick (more than likely top 5), Eric Gordon and the Timberwolves pick.
I can't recall exactly now, but I believe the original deal was Kevin Martin, Luis Scola, Lamar Odom, Goran Dragic and what turned out to be the #16 (Knicks pick sent to Houston). If you're saying the team couldn't have carved up some of those assets and go into tank mode as planned, well, I don't know what to tell you.
The Hornets didn't get two draft picks from the Clippers for Paul. You're including the pick they got from tanking, which turned out being the #1. (BTW, did the Hornets plan on trading for Gordon knowing he'd have to shut down within a couple weeks of the trade? That's some astonishing foresight by them.)
It's entirely possible in that alternate universe that they take the other deal for Chris Paul, ship Martin and Scola off to other teams for assets and financial relief, Odom still has his meltdown, and the Hornets still end in the tank and get the #1.
Gordon and the #10, vs. Dragic, the #16, and whatever else you could have gotten from Scola, Odom, and Martin. That's what I'm comparing.