If it was a reason to me it would be at the bottom. When Albertson's split I don't know which company (Celebrus or SuperValu) got to keep the private labels or if they shared them Either way it became a mute point when Celebrus bought back the Albertson's stores (plus other chains) that were split off in the first transaction.
I think that Safeway's manufacturing arm was of greater value in the deal than the private labels. With all the different companies now owned I would not be surprised if they adopt a new private label theme as Kroger has done with some of their labels - ie PSSST. Of course they have kept some of the banner labels, but most are ending up with the Kroger name on them. Avondale used to be a private label brand of Kroger as well.
When the company split, SuperValu got the "better" divisions, the store brands, and most of the debt (which would be a problem later). Cerberus got the "worse" divisions, and began to turn it around. They got rid of Dallas/Fort Worth's distribution center, the Northern California division, and most of the Florida division. For a time, most of the stores in the DFW division got AWG's store brands, though the Louisiana stores were switched out to a SuperValu warehouse. Before SuperValu sold out, Cerberus was beginning to (though no stores got this on the outside) rebrand their stores as "Albertsons Market".
Meanwhile, SuperValu had gotten rid of many existing brand names (including most items bearing the ACME, Albertsons, Shaw's, or Jewel-Osco names) with Essential Everyday. When the company reunited, SVU held much of the backoffice support and had all the store brands (like Wild Harvest, which it distributed to its own network). The distribution centers were also largely operated by SuperValu. In all, the reunited Albertsons was not the same, even if it hadn't lost 40% of its supermarkets in the last 7 years. If you had (past tense) an Albertsons store in your town, it was probably lost between 2006 and 2013.
With Safeway, Albertsons gained a pre-existing palette of store brands it can use exclusively for its own stores (O Organics, Mom to Mom, Refreshe), and while the manufacturing facilities are a nice bonus, there's none for stores outside the West Coast area (Texas, Chicago, the Northeast). (More likely, Safeway's infrastructure, like their accounting department, was a plus). It's a win/win situation because Albertsons now has a complete exclusive store brand line and Safeway shoppers can keep their store brands (a very rare situation in most cases, usually the acquired company sees their generic product line vanish). For the first time in a decade, Albertsons can present itself a unified company ready to take on Kroger and the rest...but it just is not the same anymore.
Anyway, P$$T and Check This Out are the "super low end" items, usually what they'd put on things like the brand of chocolate chips that are actually just chocolate-flavored sugar, or the small packages of single-ply toilet paper, and Safeway does have something like that, Value Red, which it introduced a few years ago. (There's a blog post with a mayonnaise jar with just the logo and the word "MAYONNAISE", generic packaging at its finest).