Boiling, however, is also a key part of the brewing process and it does a smashing job killing germs....

1% isn't that low though. I'm sure you could drink a lot of that, so people did get drunk.

"It was common for workers (including sailors) who engaged in heavy physical labor to drink more than 10 imperial pints (5.7 litres) of small beer during a workday to quench their thirst. Small beer was also drunk for its nutrition content; it might even have bits of wheat or bread suspended in it. Erasmus Darwin, in his A Plan for the Conduct of Female Education, in Boarding Schools of 1797, thought that "For the drink of the more robust children water is preferable, and for the weaker ones, small beer ...".[5] Larger educational establishments like Eton, Winchester, and Oxbridge colleges ran their own breweries.[6]"

So even if you drank 10 pints of 1% beer, that's equivalent to 2 pints of 5% beer. Spread over a day, I don't think 2 pints is getting anyone drunk at all, except maybe for children who somehow got their hands on 10 whole pints of 1% beer.