I don't know who in the thorium boosters' club started the "light water reactors were meant for weapons plutonium" meme but it's nonsense.
To quote "Technologies Underlying Weapons of Mass Destruction",
Reactor-grade plutonium recovered from civilian reactors differs from weapon-grade plutonium in the relative proportions of various plutonium isotopes. Reactor-grade plutonium has a higher rate of spontaneous fission reactions than weapon-grade, generating neutrons that can initiate the nuclear chain reaction during weapon detonation sooner than would be optimal. As a result, using reactor-grade plutonium in a first generation nuclear weapon can significantly reduce both the predictability and the expected yield of a weapon designed by a proliferant state.
None of the states that have either made nuclear weapons or attempted to do so appear to have selected anything but high-quality plutonium or uranium for their designs. Nevertheless,
from a technical perspective, reactor grade plutonium can be used to make nuclear weapons, and any state possessing significant quantities of separated plutonium should be considered to have the material needed to fabricate nuclear components for nuclear explosive devices in a short period of time.
http://www.au.af.mil/au/awc/awcgate/ota/9344.pdf
If you want to seize on the part where it says that one could build bombs from civilian reactor waste even though it's less straightforward and no nuclear weapons state has ever done that, then I'll point out that the thorium fuel cycle likewise could be used for bombs even though no NWS has ever taken that path (Quoting LANL's "Thorium Based Power Systems and Relevant Safeguards Considerations"):
Thorium is not safeguarded until it is converted into fuel materials. It would seem that if the starting point for uranium safeguards is moved up and thorium begins to play a larger role in the global nuclear establishment, then thorium safeguards should move to the equivalent point in the thorium fuel cycle.
Unlike thorium, U-233 is subject to stringent safeguards. An SQ of U-233 is only 8 Kg, the same as plutonium. U-233 is a highly desirable weapons material despite any practical U-232 content. According to the material attractiveness studies done at LANL, PNNL and LLNL, the additional dose from U-232 decay products is insufficient to stop a determined adversary. While it may be somewhat beneficial to physical protection, the dose rate is not high enough to incapacitate workers. Dose rates can be greatly reduced with shielding and military personnel handling a fabricated weapon should be able to have reasonable dose rates using established techniques. For example, the pit can be stored in lead shielding and only placed in the weapon immediately before use.
http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lare...
The actual military lineage of civilian LWRs is that the US Navy developed pressurized water reactors fueled with enriched uranium to power vessels in the 1950s, starting with USS Nautilus. That variety of reactor had the fewest unknowns when the civilian nuclear industry first developed in the US and the path dependency effects continue today.