With low frequencies, directionality is negligible, so it's not about turning it "toward" the wall, but about placing it against the wall. I suppose it's possible that the sound radiates more from one side than the other (possibly the side with the cone, or maybe the side with the port if one exists!) so turning it can result in effectively moving it closer. Or maybe you were listening to a more directional frequency range than I'm thinking of. Anyway, why does closer matter?

If you suspend a subwoofer up in the air so it has no boundaries, its sound radiates in all directions (full space). If you put it on the floor (let's assume all such boundaries are infinitely dense and thick, for simplicity) its sound now radiates only upwards/outwards (half space). Now push it up against a wall: quarter space. And finally, put it in the corner of the room: eighth space. Of course for a few millimeters it goes toward the boundary but then is reflected back, and so long as the distance isn't so significant relative to the wavelength that destructive interference (cancellation) occurs within the audible range, all interference is constructive (additive). The SPL in the listening area increases by 3 dB for each of these boundaries/halvings, although in practice it's slightly less since typical boundary material is a little bit acoustically absorptive (sound converts to heat) and acoustically transparent (sound is transmitted through to the other side), but even complete absorption isn't any worse than complete transmission to a place with no listener (i.e. the absence of a boundary): the sound goes unused either way.

Fun fact: typically half-space is used when citing the efficiency of a speaker in terms of dBSPL/Watt, since the vast majority of the power is for bass, and it's considered rare to emit bass against fewer than one boundary (the floor).

The next time you are deciding where to position your bluetooth speaker, if it's lacking in bass, boundary-load it.

But this is all about turning non-directional sound into directional sound (through boundary loading, which is a very close cousin to horn loading, as a sibling comment mentions with folded horn cabinet designs). TFA isn't about that though, it's about sound that's already directional! So I doubt any of what I've said is relevant to this mysterious effect.

Couldn't agree more. But even as a bass head myself (living room flat to about 27 Hz) I find myself occasionally somewhere with a portable speaker, like when traveling... Someone puts it on a table and starts playing it, and is blown away when I move it to be against the wall. The -10dB point moves from, say, 200Hz down to 150Hz.

As for cone size tradeoffs, an interesting peculiarity is in live music: 10" is most common in bass rigs (assuming 4+ of them in a cab) while 12" is most common in guitar rigs. Go figure. Ultimately, the combination of driver specs and cabinet volume can be tuned for any desired response, within reason.

Bass speakers are not directional. Near a wall, air cannot displace, only the pressure can vary. When standing waves form in a room, the places near walls are nodes with respect to displacement. That makes them antinodes for pressure. A speaker next to a wall is in a pressure antinode for standing waves of multiple frequencies, an ideal position for driving those waves.

Corners maximize this effect. A speaker in a corner where two walls and the floor meet is in an ideal position to drive standing waves along three axes.

I suspect, turning the driver toward the wall helps it get closer to the wall, and to create pressure in that space.

some bass bins are in a folded configuration so that the speakers are not firing directly out of the front of the cabinet but from an angled position that hits the back before exiting the front of the cabinet.