>Try always and tell the truth
I think the article is incorrect on this though, try always and tell the truth is a perfectly fine albeit slightly anachronistic usage that would mean
Whatever you do you must always try (that is to say not give up), and tell the truth.
One might also assume that you should tell the truth about trying always is the meaning, but at any rate it is not a phrasing that would be out of order a few hundred years ago.
That's not the point. While it's a valid sentence, as you point out, it means something different from "try and always tell the truth".
In contrast "try to always tell the truth" and "try always to tell the truth" are both valid and mean the same thing.