So, into the hex and no bog check because he's not "entering" the rubble hex?
I think your OP question has been answered above. A closed-top AFV in bypass of a rubbled building would take a bog check (B24.121). Non-armored or OT AFV would be destroyed. Really, the rubble rules are a bit vague as neither B24.11 nor 24.121 explicitly state that a bypassing AFV is subject to "falling rubble" (and is certainly NOT an "occupant" of the rubbled building), but I can't see another way to make sense of them (B31.15, btw, kinda implies that this is the correct way to interpret the basic rubble rules for bypassers of any building).
As for where to put a surviving vehicle, the RB doesn't say. It makes the most sense to say that the vehicle is no longer in bypass and is therefore now IN the rubble hex. This is how I would play it, but it certainly could use a Q&A to confirm (sorry to everyone who has already come to the same conclusion...I must be slow!
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Indeed, the more I think about this, the more I am unsatisfied with that answer. Suddenly "moving" an AFV from a hexside CAFP into the hex proper can create now-you-see-em-now-you-don't situations which seem a bit too weird. Infantry often move abruptly from bypass into an obstacle (whenever pinned/broken or unloaded in bypass), but at least those moves are realistic enough and done within the confines of their own movement phase. While the RB states no such thing, a better rule might be to let the AFV remain "in bypass" but unable to expend any MP other than to start, delay, fire, and/or to leave the hex.
As for Brian's question: vehicles "in bypass" on a narrow road when the building on the adjacent hex (but same hexside) is rubbled creates a worse problem. Besides the rubble rules themselves (particularly B24.121), the operative rules seem to be the following:
B3.43 A road covered by rubble/debris (O1.3) is treated as non-existent
B31.15 RUBBLE: Placing a Rubble counter in a hex that contains a Narrow Street hexside eliminates any roadblock across that hexside, affects all units/equipment currently in Bypass (in either/both hexes) along that hexside as if they were hit by falling rubble (i.e., as per 24.121), and eliminates all mines along that hexside (in both hexes).
B31.126 RUBBLE/BLAZE/WRECK: All Bypass along a Narrow Street hexside is NA if either/both of the hexes forming that hexside contain(s) another vehicle/wreck in Bypass along that hexside, a Blaze counter [EXC: burning wreck along another hexside], and/or a Rubble counter. No wreck (or Immobile vehicle) on a Narrow Street may be removed as per D10.4.
After thinking about this, I don't think I like moving the bypassing vehicle afterall. There definitely needs to be a Q&A on this and an errata issued as it makes little sense to do anything beyond the requirements of B31.15. Absent any official ruling, I think I would play that any surviving vehicle in bypass (on the far hexside of such a rubbled, narrow street) would remain in bypass on the hexside. However, the road itself would cease to exist and be considered rubble as per rule. Once the vehicle exits, bypass of that hexside (either side) would no longer be possible.