They are not joking, and some cars cannot adjust the angle or lateral position of the headrest without replacement. There are cars (like 2009 Lincoln MKZs, cough) that have headrests and seats that look and feel exactly like the image.
I owned one for about 3 years, and I still blame it for starting my weird neck/shoulder problems years later.
Aside from the tropes that were the major plot arc, I found Picard to be an enjoyable watch.
What else are people hating on it for?