If that were the case, then I believe the characteristic would say "Likes to thrash about". I remember reading on some Spanish site (I followed it from the Resourse Thread, iirc) that if you get a Pokemon whose has repeating IVs, certain stats have a "priority" over others, and it'll show that one. For example, if I breed a flawless HP, Def, SDef Chansey, the characteristic would be "Often dozes off". However, if I had that same Chansey I bred it to have flawless SAtk, Def, and SDef, it would say "Capable of taking hits".
According to what I could make out, the priority of a stat basically goes in the order that they are listed in the Pokemon's summary. So HP>Atk>Def>SAtk>SDef>Speed
Hope I helped.
Edit: As for evidence, my brother got a shiny Mild Deoxys from someone. It had 31 in all IVs (an obvious hack, I know), and the characteristc was "Often dozes off".
If that is true, then how do you explain the following, and other similarly-documented characteristics?
I don't remember said:Here's a rundown of multi-flawless pokemon I have in pearl:
Feraligatr: hp/defense/sp.atk/speed = Capable of taking hits
ralts: hp/attack/sp.atk/speed = Mischievous
Pikachu: hp/sp.atk/speed = Alert to Sounds
Smeargle: hp/attack/speed = Often dozes off
ralts: hp/attack/speed = Alert to Sounds
Gligar: hp/attack/defense/speed = Often dozes off
etc. etc. Believe me, I tried to find a pattern, but I couldn't find any. It is probably random, or else it's so subtle that I cannot pinpoint the pattern without hacking the ROM.