It's pretty much a myth (other than in theory) - as long as you use the same type LED's, and parallel at least three (or more - the more the better) then the current shares out quite nicely. But don't order different LED's from different sources, and expect everything to work out well.Those LEDs are connected in parallel not in series, a very big difference!
I am afraid this makes things worse.
Connecting two LEDs in parallel is much like connecting two diodes or Zener diodes in parallel. The slight difference in their V-I characteristic lets their currents be different noticeably, as Dana pointed it out (post #19).
But regardless, Ron's suggestion in post #18 is what the OP should be looking at - if you've got enough supply voltage, then use it, and make everything more efficient.