No, it implies that the parent title was "Re^n-a: New title (Old title summary)", that is, until you engage your brain in a non-trivial fashion.
There are two ways to interpret "Re^5:" on the front of the node. You can consider it part of the text that most closely follows it, but that leads to replies that have no "Re" in front, which I personally find annoying. Better, IMHO, is to interpret the leading "Re^5:" as an inviolate indication of the node's depth in the thread, not the level of depth in the most-recently-declared change of subject. I'm usually more interested in the depth within a thread than I am in the depth relative to a title change. And as long as it goes along the lines of from "Re^4: Original topic" to "Re^5: New tangent (orig topic)" to "Re^6: New tangent" then the relative relationships make sense.
In the short term, if I'm interested in a thread, then the above "Re^5:"-to-"Re^6:" transition is either in my memory or on my screen so the connection makes sense and I likely am aware that the "Re^5:" was where the subject change was first reflected in the title and so am also aware that "Re^6:" is an immediate reply to the declaration of subject change.
In the long term, when I search, "Re^6:" tells me that the node is fairly deep in a thread, which gives me a good clue about the character of the node. That gives me a better clue (in my experience) about the node than the information that it is a first-level reply to a declared change in subject within a thread.
So I prefer that style both in the short term and the long term over the pattern "Re^4: Original topic" to "New tangent (Re^4: Orig topic)" to "Re: New tangent".
And I'm not a big fan of accumulating increasing amounts of baggage in node titles. So I like the idea of at least eventually dropping the link to the original title when the subthread as truly, fully wandered away from the original subject (which would also mean dropping the original "Re^$x:" indication and thus losing information that I often find quite useful).
And I am a big fan of fairly frequent, minor adjustments to node titles (as is clear from my posting history) so I actually hope to run into the problem of going through "Re^3: Best practices", "Low-orbit junk (Re^3: Best practices)", ... "Re^2: Low-orbit junk (Re^3: Best practices)", "Orbital maneuvering (Re^2: Low-orbit junk) (Re^3: Best practices)", ... That either leads to really ugly, long node titles or to the trailing junk being dropped and there being no indication that the node is deep in a thread. So that is another reason why I'd like to set up the expectation that the leading "Re^$x:" is meant to be an inviolate indication of depth in thread rather than something to be moved/disgarded whenever a subject change is declared.
I wouldn't be too surprised to one day find the "Re^$x:" factored out of the form input box (most of the time) where the title can be adjusted so that it actually becomes inviolate (after all, we need to make the system proof against fools rather than try to make metaperl not behave foolishly, ya know?).