It is one of those "one person's X is another person's Y" comparisons: indoctrination/brain-washing, religion/cult, freedom-fighter/terrorist, cute cat / insane evil sharp edged ball of allergens, ...
A more passive form of indoctrination would be repeated explanation (with or without query/prompt) so explanation can become indoctrination depending on context, but I'll stand by my choice of words above.
"Where do rainbows come from" can be answered with the explanation "As a way to show God's promise to Noah never to flood the Earth again" or with the explanation "because sunlight refracts through water into all the different colors we can see" or with the explanation "invisible unicorns fly through the sky sometimes and leave rainbows where they've gone".
Many people would call one or more of these indoctrinations, despite the complete lack of "should" in any of the responses. Egocentrism does not a benignity make.
Besides, just as you hold your "must be provable" views dear, similarly the religious parent holds his or her religious views dear.
Adults just slow down the writting but we always try to fit in the social group that we are living. And that includes political opinions, faith, etc...
And if I had to choose between that kind of Chinese brainwashing and Guantanamo/CIA black sites, I'll pick the Chinese option.
Patriotism being one example of this type of propaganda -- the idea that some of us are better than others because we were born on one side of a line in the dirt.
And often each system of beliefs has epistemic protection against debunking... for example, religious believers may view debunkers as agents of evil/Satan, while conspiracy theorists may view debunkers as agents working on behalf of the conspirators. In both cases, one has a "rational" reason to be skeptical of (or even outright disregard) any arguments that attempt to undermine one's axiomatic system.
The more a person seeks the opiatic, emotional feeling of fake knowing, the more receptive he is to religion, political brainwashing, conspiracy theories, prejudices, social authority structures, etc.
And when you're comparing the US of 1950 to the Communist China of 1950, frankly, if the pro-US viewpoint is naive, the pro-Mao viewpoint is utterly deluded.
You still run into the kind of people who try to draw moral equivalence between the Japanese internment and Dachau to this day. I'm not saying this to deflect criticism, because I hold the US to a much higher standard than the rest of the world and the way to do that is to be critical. But coming to the conclusion that the US used chemical weapons in Korea (we didn't) or that Mao was a positive force for China in the 1950's (he wasn't) just because America falls short is a very long way on the opposite side of reasonable.