That is not at all what MMT says and I don't understand how an honest reader of the MMT literature would arrive to that conclusion.
What they say is that public debt and public deficits are irrelevant (there goes your "outlandish true" of balanced budgets) but they also say that inflation is the most important constraint in public spending.
>> And that's obviously true, to the extent that people are willing to accept that money in exchange for their goods and services (an extent which is not infinite)
In the MMT framework, there is always demand for the currency in what taxes have to be payed. That's obviously true. That doesn't mean that inflation is not a factor.
By the way, most cases of hyperinflation in history, including the infamous Zimbabwe, are due to a supply shock (http://bilbo.economicoutlook.net/blog/?p=3773).