I think the confusion here is over "visa" vs "status". The OP in this thread is talking about getting a new visa stamp (a card with a picture glued onto a passport page), the USDOS link you post talks about extending your status in the country (they use "visa" term because most people confuse the status and visa, but the form I-539 on that page is the EOS form and does not do anything to the visa). The latter is possible anywhere, the former is only in a consulate.
there is no confusion, my argument is that this is only true for the US. according to my experience no other country does it that way because in most countries, visa and status are one and the same thing. no visa, no status. or, if there is a difference, then extending your status also extends your visa, or vice versa. and you do it in the country. not outside.
i also reject the claim that there is no one inside any country that could verify the status of a foreigner, only consulates outside the country could do that. that is straight out nonsense.
How do you physically "extend" a visa? Do other countries have visas where you can print a new expiration date? You mentioned China, and I looked up images of a Chinese visa, there doesn't seem to be a place to put a new date, it has one field after 'Enter before', are you sure you got a new visa stamp with your extension of status?
i also reject the claim that there is no one inside any country that could verify the status of a foreigner
A US visa stamp is only issued in a consulate. It's true.
A question not being true is a novel concept to me. I was genuinely curious what country has an office equipped to interview and background check any foreigner in the world. But apparently it's not true, whatever that means.
You also proclaimed that one can "renew" a US visa in the country. You seem to be reading something that is not written and knowing something that is not true. Good luck with that!
sorry, renew and extend don't really mean anything different to me, because the end result is the same: you get to stay longer. i don't see why they should be different and why that should matter.