I used to disbelieve the idea, as it has all the qualities of a nice myth. Turns out that I was wrong. And also, that the story behind it is more complicated than the myth makes us believe.
A nice example can be found on scientific papers published in the area of commercial food technology, like this one. An important quote from the abstract:
Stickiness and consistency of doughs made from low-moisture flour were more sensitive to changes in dough water absorption than doughs made from flours of high moisture content. Dough water absorption level was more difficult to adjust in doughs made from low-moisture flours.
So, to answer the first point: yes, it makes a difference. If your house is very dry, this will change your dough. I am not a specialist in that area (did not know that there is a unit for measuring stickiness!) but I guess the difference will be noticeable to a home cook too.
Now for the second point: the usual interpretation is that "some water is missing, so just add it back in". That turns out to be wrong! The problem is not the tiny amount of missing water in total, it is that dough made from wetter flour reacts differently to added water. Dough-from-wet-flour is stickier, and also reacts less sensitively to changes in the added water.
So, can you counteract the effects? To some extent, yes. Adding a tiny bit of extra flour if your dough is too sticky on a given day, or slightly adjusting the amount of total liquid in doughs that are supposed to be dry, like shortbread crusts, can make the difference between dough you can work with and something that cannot form a ball no matter what you do. Still, getting the perfect consistency might not be possible with any dough.