Hi Mehul , Im not a expert mate , on looking at 20 + "Lee Speed" marked sporters , all were made/marked BSA&M.Co or BSA.Co and only had the dust covers marked by who ever !
A heap of the BSA sportes are only marked "BSA .Co" but we would call them Lee Speeds to look at !

That one you saw would be different & may be they had a deal where they could remove the BSA part ?

The only other company I have found who made commercial sporters , were LSA , who did some deal with BSA in the day (or so I read) later Parkers & later still Parker-Hale , who made sporters on all actions , even Ex Mil . I was told by elderly BSA Gunsmith & read in some of his literature that BSA would make a sporter on your rifle if you sent it in to them , so who knows for sure , not me any way !

Not much help Im sorry , I should really sit in the corner and keep quite . LoL !