Earlier this year, I speculated that B3 may have been originally written for Holmes Basic, based on the date of publication and that the author Jean Wells ran a Basic tournament at Gen Con in 1980, before the Moldvay set came out in 1981.
Today I came across a post by Frank Mentzer from 2008 in his Q&A thread on Dragonsfoot that actually verifies this:
"Mike wrote B1 pretty much based on OD&D but modified it a bit when Holmes was finalized. Gary wrote B2 as a replacement for B1; he decided that the starter module shouldn't be stocked by novice DMs. When Jean wrote B3, she was working off Holmes but transitioned to Moldvay. (I was involved with B3 somewhat.)"
Interestingly, the green cover B3 revised by Tom Moldvay contains a short paragraph on using the module with Holmes Basic; it basically just assures the DM that the module can be used as-is with the earlier set.