My guess is that it originated with late 20th century back and forth over exclusive psalmody; was the Westminster assembly an assembly of exclusive psalmodists? etc. Rowland Ward made a similar argument in a note to me in 1998 (he's EP, or was then, but found the line of argument unsound; he linked the necessity to understand psalms as "praise" in WCF 21.5 to explain the other scripture song project initiated by the Scots the same time they were refining the WA's psalter, which eventually became the 1650 Scottish Psalter; he later conceded to me as we both were exposed to the MSS in working with Chad Van Dixhoorn, that lack of capitalization was not a sound argument). The most prominent online source I am guessing originates with Stephen Pribble in his 2001 article, though it could be he uses the argument without crediting a printed source, especially if Dr. Ward was making it a few years earlier. You could conceivably get away with hypotheticals about lower case psalms since few had seen the manuscripts or first printed texts of the assembly's productions nor understood that one cannot rule out printer's doing either case willy nilly depending on their available type or druthers, since printers hand the primary hand in these things not the authors.
Scott Clark has said, "I searched about 114 orthodox Reformed texts (from Junius, Perkins, Bucanus, Cartwright, Twisse, Gilespie, Diodati, Paraeus) from 1600 to 1640 and found no obvious evidence of
psalm used to include an extra-canonical song."
https://heidelblog.net/2014/09/what-did-the-divines-mean-by-psalms/
Pribble's article is still up there without any modification so it of course lays seeds of that thought, gets repeated, etc. and those happy with that never look further, though folks have been rebutting this argument for nearly the same amount of time this idea has found currency.