What Pivotal does is fairly vanilla Extreme Programming. Indeed, the vanillaness of it is something of a selling point. In the London office, we would start projects by giving client PMs and programmers a copy of Extreme Programming Explained and telling them that was what we were going to do. It's easier to coax them into following a process if it's a documented industry-standard one rather than some special sauce.
Pivotal does have a few extra bells and whistles that fill in spaces around the XP core - "discovery and framing" [1] and "inception" [2] being two that spring to mind. And as you say, there is less emphasis on iterations as a unit of work - the planning meeting is weekly, but it feeds a continuous flow of development and delivery. But the daily pattern of work should be familiar to anyone who knows XP.
[1] https://content.pivotal.io/blog/what-we-did-on-our-summer-in...
[2] https://www.infoq.com/articles/project-inception-meeting/
In my experience more typical is that the PM chooses a set of tickets and asks the team whether they can commit to them.
According to the constraint above, neither that, nor the “pick from the backlog” process you’re describing would qualify as “Scrum”.
At Pivotal, the forecast of what will be delivered changes all the time and it is tracked in a single tool that everyone can look at and keep up to date with (along with a few short meetings to keep everyone on the same page).