Yeah that DHS screenshot is fake. If you boost the exposure there's conspicuous gaps in the JPEG artifacts around the fields where they were edited.

They would have got away with it if they just used Inspect Element!

The same head of product quoted in the sib comment admits that "for a small set of accounts the location data was incorrect". Given what we know about Twitter's relationship with the government and this administration in particular, you're simply left to do with that information what you will.

I personally do not trust Twitter, or the government, very much. I also would not be surprised if some government accounts were created at various embassies around the world or through strategic VPN networks, or if general business is conducted through a darknet-like node system which includes allied endpoints. To me those are more plausible.

Does this make the fact that it showed as Israel, was disabled, and is now "corrected", mean that this feature is good or bad?

Either we can trust all location data all the time, or we can trust none of it. We cannot expect Nikita Bier to swoop in on every suspicious tweet and try to educate us on IP range changes and DNS glitches or whatever.

Furthermore is it more likely that a small set of special accounts seemingly never collected location data on signup, or that for a small number of accounts X simply modified that data post-hoc?

Blink twice if you are in danger.