GCC-
Yes, the 707 has a larger cross-section than the Air Force version (C-135/KC-135 etc. etc.) The whole family started as a project to produce a jet version of the C-97/KC-97 Stratotanker, and originally had the same cross-section dimensions as the KC-97 except that the 'crease' at the cabin floor was smoothed over.
The USAF made Boeing enlarge the cross section, and then the airlines required an even larger section. So, the 367-80 has the smallest section , then the KC-135 is larger, and the 707/720 is yet larger again.
FWIW, the KC-97 was essentially a B-29 design (tubular fuselage) with another, larger tube grafted on top.