If this was sent out or this tone/demeanor used in one of the early education grades, I would have a huge issue with it. For middle schoolers at the end of the year, it doesn't bother me so much, though it I think it should only have been sent to those kids who it applied to (may have been, so not really judging that). There's a huge difference in how I think it's appropriate to address late work and students in general in early education vs middle school.
In 1st grade, DD came home crying frequently. It took a while to figure out that she was uncomfortable around and a little scared of her teacher. We finally figured out the problem when she said that kids (not even her, but other kids) who did something wrong were made to sit on a bench and write sentences. The teacher would then go over and make a big spectacle in front of everyone, put her hand on her hip, and say, "I can't wait to see your sentences." Doesn't sound too bad on the surface, but she was using a sarcastic tone that DD and some of the other kids didn't understand and thought the teacher was making fun of them/getting joy out of them being in trouble, and apparently that tone/attitude/hand on hip mannerism was frequently used throughout the day. I witnessed it myself when I came in to talk to the teacher about a page in their journal they were told to skip and save for a "special assignment." They were told to do this on a day DD was absent and she found out from another student after she did her next assignment on the page that should have been skipped. Seems like a minor issue, but DD was petrified she was going to miss out on something when they came back to that page or get in trouble and kept trying to ask the teacher what to do, but the teacher kept dismissing her. So anyway, when explaining that DD had been coming home crying afraid she would get in trouble over it/miss out on the special assignment it was saved for, the teacher cut me off, put her hand on her hip, and told DD sarcastically, "If you would have done it correctly the day it was assigned to everyone, you wouldn't be in this situation. Everyone else skipped the page, so maybe you need to pay better attention when I'm giving instructions." She continued on for a few mins while my jaw hit the floor and DD hung her head in shame. Once I collected my bearings, I reminded her DD was absent the day she told them to skip it, had asked her several times what she needed to do, and that a 6 year old shouldn't come home crying because of a page in a journal. I told her if necessary I'd buy her a new journal and have her copy all the work, but that she would resolve this with DD TODAY. I then sent DD away and told the teacher, "There's NO reason for a teacher to speak to a 6 year old in this manner and it will not continue."
Obviously, that was a different scenario to what's being discussed in terms of an accident in work due to absence vs trying to bring a grade up after not doing work all year. I shared it to show that there are some teachers that seem to have a superiority complex and don't speak appropriately to kids, but also that in my opinion what's acceptable in speaking to a young child who's still learning the ropes is far different to that of a middle schooler who knows what they need to do and has failed to do it. Had DD been 12 and asking for extra credit after not doing the work all semester, I wouldn't have had issue with the teacher addressing her like that.
I think the teacher (in the article) could have chosen to set an example for the kids by displaying more tact, but overall don't have a big problem with what was written. I think it would be inappropriate if everything/everyone in class was dealt with using a negative tone. Just sending a strongly-worded letter concerning extra credit that had likely been asked about several times by students who didn't do their work is understandable to me.