I’ve owned a PA-28-140 with the 30’ wing and a similar PA-28-180. Neither airplane is really a four place airplane even under normal conditions. The only thing those airplanes do good is come down out of the sky. An even worse airplane I owned was an AA-1A … THAT was a 1/2 person airplane. 
I once took off in the 180hp PA-28 at the 9,000’ Grand Canyon airport with 2 aboard and had a heck of a time trying to climb out of ground effect. Recently, I had to decide whether to sell the 140 or a 172 I’ve owned a long time … I sold the 140 for this reason. I once took off with four adults on a hot summer day at Edwards AFB and the 172 performed just fine, by comparison. Problem is, ya gotta fight that airplane to stop flying, by comparison.
Can’t say if density altitude had a hand in this tragedy but I’d bet that it did? RIP.