I think there's different methods at play here.
The article is clearly talking about making tea in a pot. Which if you do, gives you the option to let the tea brew in the pot before putting it into the cup and whether you put milk in the cup first or last it's not going to affect the brewing of the tea in the pot.
When you make tea in a mug with a teabag, it's a different matter because putting milk onto a dry teabag in a cup, then pouring the hot water on is clearly going to affect the temperature of the liquid in the cup, thus affecting the brewing of the tea.
So if making tea in a mug, always put the milk in after the tea.
I can't stand milky tea or tea that's not brewed for long enough, what's the point if it's not got any flavour?
As for sugar, I always put sugar in the mug with the tea bag and then pour on the water, because sugar dissolves better in boiling water than in water that has cooled down.