I've been working on my neighbor kid's Murray USA (old school) and the headset is rusted/missing bearings, and just plain shot. The fork has a 1" threaded column tube. I got an Inline 1" BMX Threaded Headset replacement for it. Got ready to do the job, poped out the old races and discovered they are bigger than the replacements. The old races are 34mm OD and the head tube has an ID of 33.8mm. The new headset races are 32.6mm. Everything I find has the same races for a 1" column.
From everything I can find on the 'net, the headtube is sized for a 1-1/4" column tube. BUT, the current fork and headset are 1".