I don't understand this theorem about covering spaces or it is a typo?

Question

Isn't it a trivial conclusion the first part of the following theorem from Theodore Frankel book (The Geometry of Physics: An Introduction) or it is a simple typo?

Theorem: The orientable cover of $M$ is always orientable. The number of sheets is $1$ if $M$ is orientable and $2$ if $M$ is not orientable.

Answer 1

I find this paragraph on the page 573 in the same book:

... If $M$ is orientable, then the covering obtained reduces to $M$ itself, but if $M$ is not orientable we obtain a new space $\overline{M}$. In any case $\overline{M}$ is called the orientable cover of $M$, for, as we shall see, this $\overline{M}$ is always orientable.

So the theorem is correct.

Answer 2

Whether this theorem is trivial depends on the definition of orientable cover. With that name one would hope that it is orientable but if that is not part of the definition than it has to be proven.