To give you a better perspective, if you were traveling back then, border control will be the only deciding body of whether you make it or not. Nowadays, you only show up at the border if the "State" has determined that you are admissible. Border control still has a say in the matter but that's power is getting smaller and smaller.
It's a paradox, because while the bureaucracy has increased and ossified, there was a lack of accountability back then. If the teacher of that school decided that you are inadmissible, you are pretty much out of option.
Finally, here is an excerpt from Wikipedia to show you how much things have changed:
> During World War I, European governments introduced border passport requirements for security reasons, and to control the emigration of people with useful skills. These controls remained in place after the war, becoming a standard, though controversial, procedure. British tourists of the 1920s complained, especially about attached photographs and physical descriptions, which they considered led to a "nasty dehumanisation".[19] The British Nationality and Status of Aliens Act was passed in 1914, clearly defining the notions of citizenship and creating a booklet form of the passport.
For "elementary" grades it would be primarily by function (can read? can write? can count?) rather than age. And it would not be uncommon to have a much older kid from a poor family sit with little kids at the "cannot read" table.
In this setup jumping a grade could be as simple as sitting at the next table. Can read -- go there. Can count -- one more step. Physical development came from carrying water, herding cattle, bringing and splitting firewood, etc. outside of school.
And the grades mix/don't mix on their own volition at lunch and recess, anyways.
Those schools existed for two reasons: a) to teach kids how to read and write and some very basic math b) find ones with potential and connect them with benefactor to sponsor theirs more advanced education