The problem is that any changes to the back and sides tend to have a relatively small effect on tone and volume (compared to changes to the top), so it's always difficult to say anything definite about the effects of such changes. Hence phrases such as "perhaps" and "some feel . . ." which is frankly more honest than saying anything more conclusive.
Having said that, I don't think there's much debate that making the back (and sides) heavier and stiffer will result in more of the string energy being transferred to the top. The question is, does this make a significant difference to volume, and does it affect the tone?
This is Smallman's approach, of course, making not only the back and sides very
stiff and heavy, but also much of the top - with just the lower bout of the top being very thin and light. This combination of very light (lower bout) top and bridge, and very heavy everything else, is what gives Smallman's (and similar designs) their volume, rather than the lattice itself, which is simply a means to the end of producing a really light top. At this extreme, most would agree that volume is increased, and that tone is affected (for better or worse), but again, I would say that the top has the far greater role in these changes than the back and sides.
There is also much confusion, as different makers use different terms to describe the same things, and the same terms to describe different things (we like to keep the punters guessing
). So a double top guitar may be a composite top, or may have a second top somewhere between the top and the back. This may also be called a double back, which could also be a laminated back. Confused?