It was likely rigged. I'm having a tough time finding anything that definitively says that, but it's certainly implied to be so. If only because Mongolia held a special significance for the Soviet Union and its status as an 'independent' country was already predetermined at the Yalta Conference of 1945 and with the Sino-Soviet Treaty of 1945.

I'd point out the Mongolian People's Republic was pretty firmly a Soviet satellite, yet it wasn't without a will of its own. The Sino-Soviet Treaty of Friendship and Alliance was signed with the Republic of China (as in, the Nationalists, not the Communists), who still entertained notions of keeping Outer Mongolia in the new China, for a couple of reasons.

(quick clarification here...modern day Mongolia is sometimes referred to as Outer Mongolia. Why? There is a massive province within China called Inner Mongolia that was historically part of the core Mongol Empire.)

SO, Chiang Kai-Shek wanted Outer Mongolia. On the other side, Mongolia's Communist government wanted INNER Mongolia. And on top of all of that, Stalin did not want the Soviet Union to touch China's borders too much. The Mongolian People's Republic would be a perfect buffer state. So it went that Stalin got Chiang Kai-Shek and later Mao Zedong (in a separate treaty entirely from the one signed with the Nationalists) to agree to the 'status quo' on Mongolia's status, which is also in the wording of the Yalta Agreement. This also lessened the chance Mongolia as a satellite would shoot above itself at Inner Mongolia or vice versa.

The actual Sino-Soviet Treaty on the matter is fascinating because it was signed in the middle of the Chinese Civil War, which meant Stalin signed a deal with the Nationalists, but had to agree to stop helping the Communists. Of course he didn't stop, and indeed signed a similar treaty with the Communists. To, basically, cover his bases. The treaty's exact provision? Both sides would accept the independent Mongolia as is, BUT a referendum on independence had to happen. It's not dissimilar to agreements Stalin made on European territory liberated by the Soviets: elections were supposed to be held. Of course in THAT side of Eurasia, that didn't really happen...there were massive irregularities. The same likely happened with the referendum you're asking about, esp. since there were ZERO votes against. HOWEVER I feel silly because I can't find a good source to say just that.

Source: 1. Ballis, W. B. (1951). The Pattern of Sino-Soviet Treaties, 1945-1950. The ANNALS of the American Academy of Political and Social Science, 277(1), 167-176. doi:10.1177/000271625127700117