That might be the case but I have been turned back before in Kyrgyzstan and was miles away from the Chinese border. Never been to Mongolia and read about border permits so I thought I should obtain some this time rather than having to be turned back.
For the two NP I mentioned and the far east of the country I will just suck it and see.

In 2010 I applied with three fellow travellers (in two cars) for the Altai Tavan Bogd NP permit. We got it in Olgi with no issues.

There were several other border areas I wanted to visit; Dariganga, Shilin Bogd Uul, Khalkhin Gol and Nomrog NP, all of which, according to Lonely Planet, need a border permit.

So in Ulaanbaatar I went to the appropriate office (with a Mongolian-speaker) and was told border permits are only issued to guided groups. Bummer.

Regardless, we went to Dariganga (nice) and Shilin Bogd Uul (awesome). We kept a low profile and had no problems...

...until we got to Erdenetsagaan where we were apprehended and held at the local police station (we were allowed to wander around town but not drive anywhere). Nobody spoke English or Russian and it was a few days before I called the British Embassy and was told that there was an outbreak of foot-and-mouth and possibly anthrax and that everyone was under curfew. So it had nothing to do with being in a border zone directly, but because we were sneaking around we had missed the main checkpoints where we would have earlier been quarantined.

I never made it to Khalkhin Gol or Nomrog NP because of the epidemic. I even drove back into Russia and re-entered Mongolia in the far east, but the lock-down was still on. We had to get travel permits (tedious) and at one point drive the truck into a gas chamber, have it fumigated, then put on a gas mask (still makes me laugh) and drive it out. All good Mongolian fun.

So I would not worry too much about creeping into border zones, just be discrete and have a look at Google Maps before hand to make sure you're not going to drive into an army base. The Mongolia - China border is a bit sensitive.

EO

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EurasiaOverland a memoir of one quarter of a million kilometres by road through all of the Former USSR, Western and Southern Asia.

What documents are required for military permit in Altai Bogd?

We are traveling on motorcycles we bought from the market but which we didn't register. We have our passports, visa, and international driver's license. Is that sufficient?