Andy,
To the best of my knowledge, yes, the addition of 'this' changes the
scope. Until about 6 months ago the page selector function was part of
the Utils class and $page was pretty much global. At that time the
page selector function was moved and became part of the Theme class,
of which all themes are subclasses. $page became part of the Theme
class, too.
In all actuality, the assignment that we're talking about here doesn't
really need to be done in the individual theme class, since
Theme::add_template_vars() assigns it and $user, so individual themes
don't have to assign either variable. Mzingi and Charcoal, for example
don't contain the $page assignment at all. K2 still does, but it could
be removed.
I hope this helps.
Rick