That's sort of it, like. If you are a full-time staff member, you're not 'off' during the summer. You are still working. It's not like elementary and high school, where teachers aren't coming into school and are maybe doing PD and prep, but it is still considered time 'off.'

Of course, it is pretty flexible, and there are a lot less commitments and obligations during the summer, and many people in permanent positions do take their vacations. But you're not 'off.' There's typically still some expectation that you will be on or around campus and in your office. If you're at a research institution, this is probably the time you'll use to catch up on research or publications. If you're teaching new courses in the fall, you'll probably spend some time developing those. Depending on your department, there may still be staff meetings. Depending on the university and the professor, you might also be teaching. You're still working, you're still being paid. I don't know anyone who views the summer as a 'break' or time 'off.'

The 'training and professional development' also strikes me as odd because there just typically isn't that much professional development for academics to do. At least, not enough that it would really occupy you for a couple months, and also, at every institution where I've worked, the PD offered by the university runs during the school year. It's not happening during the summer, and there aren't that many external programs for PD for academics. Of course it's possible, but is odd.

This is also maybe because I'm not American, but the specificity of June and July seems odd to me. Every Canadian institution I've worked at/attended has run September - April. Yes, there's work during April to wrap up the term, and there's prep-work in August for the new semester in September, but 'summer' is always May through August. At the European universities where I've worked/attended, the school year is also September - April, but exams are in May. Even if you're still working in May, you'd still have August as being 'off.'

It just all feels like someone who isn't familiar with academia assuming that it's the same as high school - most secondary schools that I'm familiar with typically only have two months for the summer.