Shared tooling was to have been the case if the 707 & 135 shared the same fuselage diameter, but they didn't, so difficult to see how they shared tooling. Boeing themselves say,
depends on what version of boeing documents/newsletters/ wiki/ etc you read- compared to friends of mine who worked tooling issues in renton.
https://en.wikipedia.org/wiki/Boeing_707
The 132 in (3,352.80 mm) wide fuselage of the Dash 80 was large enough for four-abreast (two-plus-two) seating like the Stratocruiser. Answering customers' demands and under Douglas competition, Boeing soon realized this would not provide a viable payload, so it widened the fuselage to 144 in (3,660 mm) to allow five-abreast seating and use of the KC-135's tooling.
[11] Douglas Aircraft had launched its
DC-8 with a fuselage width of 147 in (3,730 mm). The airlines liked the extra space and six-abreast seating, so Boeing increased the 707's width again to compete, this time to 148 in (3,760 mm).
[12]
... this only part of story . . .
Traces of the 707 are still found in the
737, which uses a modified version of the 707's fuselage, as well as the same external nose and cockpit configurations as those of the 707. These were also used on the previous
727, while the
757 also used the 707 fuselage cross-section.
....
The 707-120 was the first production 707 variant, with a longer, wider fuselage, and greater wingspan than the Dash 80. The cabin had a full set of rectangular windows and could seat up to 189 passengers.
[32] It was designed for transcontinental routes, and often required a refueling stop when flying across the North Atlantic. It had four Pratt & Whitney JT3C-6 turbojets, civilian versions of the military J57, initially producing 13,000 lbf (57.8 kN) with
water injection. Maximum takeoff weight was ..
https://faculty.haas.berkeley.edu/leonard/Active%20Papers/What%20Killed%20Douglas%20Aircraft.pdf
....Subsequently, the development of the military KC-135 tanker and the civilian 707 diverged. First, the Air
Force demanded that the prototype’s 132” diameter be expanded by 12” for the KC-135. Then Juan
Trippe of Pan Am, wielding the threat of Douglas’ planned wider fuselage DC-8, pressured Boeing to
widen the 707’s diameter. Boeing’s decision to bring the 707’s diameter up to 148” was accelerated by
United Airline’s defection to the DC-8’s six-across seating. With the plan for a common fuselage
scrapped, but still with largely common wings, the 707 and the KC135 would share at least 20% of their
parts and tooling (Lawrence). The two were also produced in the same government plant. Boeing could
also benefit from R&D spillovers....