Anecdotally this is true for me as well. It takes work for me to stay on DL/Skyteam. My company will sometimes pay business if it's reasonable and I can't find anything reasonable for my September trip PDX-BCN; PS on DL was $3000 and PP $2000 on UA -- I booked DL and have watched that PS flight since go up to $4500 while it's sill hovering around $2000 and $2400 on UA. I'm wishing I'd booked UA TBH (I've already requaliified for PM). But hey, whatever DL is doing is working as my PS flights look very full based on seat map.
Eyeing a late November trip to MUC and can't believe how expensive Business and PE are even this far out...