Secondly, it's much more important to look at local median income and local cost of living. $1000 a week in many areas won't get you far if most of it is taken up by taxes and housing. And before someone pulls out the "well, move to somewhere cheaper", there's no guarantee that a cheaper to live location would necessarily still support $1000/week to the owner, or if there was a commute, that it wouldn't eat significantly into that income (fuel + toll + car payment which may not be required if you live locally could be well over a $1000/month).
My hunch is most people don't base it on dividing the population in to equal fractions, which is kind of how I read your comments.
Even with that there's an awful lot of caveats, though; as folks have noted, regional differences can be huge. The median income in Silicon Valley as of last year is just under $100K (despite the picture that Hacker News can sometimes paint!), but in Tampa Bay, Florida, it was just under $60K.
I'd also point out it's 15% higher than the median. How small do you feel the middle class is? You mentioned "lower middle class"; I only see them mention "middle class".
But even for the lower middle class, it rather depends on how you choose to count it, no? I've seen some economists define middle class as the middle 60%. Given that range (~$46k - $140k), they're in the lower end, if you want to hold them to that statement (that they never made).
[0]: https://www.businessinsider.com/middle-class-income-us-city-...