canadian-american's output was not licenced as a whole by parlophone, and parlophone also released licenced various other merkin record companies' product (until emi took over top rank, converted it to stateside, and shifted most, if not all, merkin (& other?) music licenced from independent labels (i.e. not from e.g. capitol, who were by then long-owned by emi; nor from motown, whose recordings appeared in the uk on the tamla motown label from emi's creation of this). it is nevertheless possible to discern more-or-less consistent policies and patterns in emi's behaviour, as regards inventing matrix nos. from scratch within certain series, for licenced recordings they had masters cut for themselves, and may have passed copies onto overseas subsidiaries from, and occasions where they most likely obtained masters cut by the originating companies, and either invented matrix nos that incorporated the original, in an existing emi-format matrix no, or used it "as was" - whether or not doing either "ruined" emi's massive filing system.
without written account and/or eyewitness explanation from inside the belly of the whale, making sense of what record companies have done is a bit like trying to guess whether pyongang or the kremlin are following sane, if brutal, foreign policies, from watching their t.v. newsreels, publicity, western & japanese accounts of radar data - and their publicly-visible actions.
if parlophone used or created a pair of non-emi matrix nos. for a single licenced from a merkin (or canadadadian) record co, and used or incorporated the merkin (or canadadadian) single matrix nos. into them, there was probably a reason for doing so.
All the matrix numbers I've ever seen for these licensed records are machine-stamped in the standard EMI style, so all the metal stampers for the records I've seen were at least made by EMI. With the (interesting) exception of some King label EPs on Parlophone (Earl Bostic, Tiny Bradshaw etc.), which have the same handwritten matrix numbers as the US King pressings. The metal parts for these were obviously sent in by King.
the (45 am-can) 5961/5962 45 matrix nos are derived directly from the canadian-american matrix nos, so it looks like emi/parlophone were sent merkin dies to fit into their stampers at hayes, rather than tapes, from which to cut their own matrices. they're continued (with some extras in the xxxxian) into the xxxxian & kiwiiian emi/parlophone release singles.
(i'm not sure why emi turned can-am into am-can - an alphabetically tidily-inclined mind, or sheer disbelief that a merkin label might put the "can" first?)