Why doubt it? People made beer at home from barley and water and mugworth, it was decidedly not expensive.
Today the Czech Republic is the country with the highest beer consumption per capita, at 140 liters per person per year. Germany clocks in at 99, and the US is at 72. In the late middle ages, the average in Britain was 300 liters per person per year.
In 1830, Americans over the age of 15 consumed more than 31 liters of pure alcohol per year. If that was all in 7% beer, it corresponds to 1.2 liters of strong beer every day. Probably quite a bit was also in whiskey, which was cheaper than milk back then.
Very true. People did drink a lot more back then (even John Adams had some hard cider with breakfast), but also, the alcohol content of their wine or beer was probably pretty low.
We also see much more recently that 3rd world countries didn't do this, either. People drank water.