I understand what they mean by "almost always." E.G.:
Statement $A$ is true $\forall x∈ \mathbb{I}$.
Statement $A$ is false $\forall x∈ \mathbb{Q}$.
Therefore statement $A$ is almost always true...
But isn't that being purposefully coy? Instead of using the label of "almost always true," why not just be explicit?
The term almost is often used in mathematics. It refers to all but a negligible amount of elements in the set, but the notion of negligible depends on the context. For the term almost everywhere, negligible refers to a set of measure $0$, or contained in a set of measure $0$. For the term almost surely, used in probability, negligible means a set of probability $0$. For the term almost all, negligible usually refers to a finite set, but in topology, negligible often refers to a meagre set, and in number theory, almost all positive integers refers to "the positive integers in a set whose natural density is 1".
Conclusion, the meaning of the term almost depends on the context, but it turns out to be sufficiently convenient to have been adopted by say, almost all mathematicians...