That is undoubtedly true of a private library which receives no public funding whatsoever. However, once you start receiving payment from public funds - collected via taxes, this equation starts to change.
No, it doesn't change anything. Have you ever tried to photograph a manuscript? Even a library like the British Library, a publicly-funded institution that is pretty open and progressive when it comes to digitization and public access, would tell you to get lost if you waltzed in there expecting to just be handed every manuscript you requested just so you could take pictures of it. They are legally capable of kicking you off the premises, and banning you from returning if you persist. All institutions are, public or private.
I mentioned earlier some of the challenges of location and access, but let's actually look at just a few of the types of libraries that DIAMM works with and see what kinds of institutions we're dealing with. Some are public, some are private, some are private but receive heritage money grants from their Government. All of them contain valuable works. (These are just a few that I've quickly researched).
British Library Manuscript Collections. Funded entirely by the UK Government. Pre-1500 MSS you need to order ahead of your visit. I have personally heard tales of people requesting a manuscript, and being told that it's on microfilm, so you have to settle for that. (If you've ever used microfilm, you'll understand what a challenge that is, and you thank your lucky stars for DIAMMs gorgeous photographs).
You will likely have a staff member hanging over your shoulder while you consult things there. You're only allowed to photograph certain things without being kicked out.
Médiathèque d'Evreux (Bibliothèque Municipale), France.. Likely publicly funded (being a "Municipale Bibliotheque"); unlikely that you would ever gain access to actually see the MSS without a good reason. DIAMM has images of a MSS dating from the 13th Century.
Bodleian Library, Oxford University (publicly funded institution). Pretty good about digitizing. However, they have only digitized a small fraction of over 500,000 music items. If you want to consult pre-1900 works you need to use their
staff-mediated service. Readers can only take photographs of certain items. DIAMM contains over 60 MSS from them.
Bibliothek des Benediktinerstifts, Admont, Austria (a
small town in the Austrian alps). Founded in 1074. Open only during the summer, out of season on request. Houses 1,400 MSS, 70,000 works from 16th C - 20th C. Manuscripts and pre-16th C. books are
kept in a "safe depot." No digitization efforts (yet) that I could see.
Schottenstift, Benediktiner-Abtei unserer Lieben Frau zu den Schotten, Austria. Founded before 1365, houses approximately 200,000 volumes, access is solely for research purposes. You can't even access a list of the MSS outside of the library, so you actually have to visit them to find out more. No publicly available digital images.
Stift Lambach Musikarchiv, Austria. Open only by appointment. Contains 700 MSS, just catalogued by RISM two years ago. Copies are made only for researchers with a defined purpose. DIAMM doesn't have them in their database, but there's undoubtedly some stuff that they would like.
Cathédrale Saint-Lambert (Liège), Belgium. Doesn't have a website, so I can't tell what they have. DIAMM has images from a MSS dated from 1388.
Eton College. Private institution with very deep pockets. Undergraduate and Postgraduate Students
must provide a letter of introduction. Open by appointment Monday-Friday, 9.30am-1pm and 2pm-5pm. Houses more than 150,000 items. You must contact the Collections Administrator if you want any images of them, since they don't seem to offer access to them on their site. The Eton Choirbook is one of the most spectacular music MSS out there, and DIAMM is responsible for giving people access to it.
Herzog August Bibliothek, Germany. The library is open M-F, 9am - 5pm. The library publishes some images online with a CC-BY-SA license (non-commercial use). However, they have
just 733 MSS digitized, out of 11,800. You must
pay to order reproductions. DIAMM has several fragments of a 14th C. Manuscript from there.
The list goes on and on and on. You may not like it, but that's the way it is in most libraries that house manuscript collections. DIAMM works within their terms and does incredible, amazing things. It seems to me that you don't understand the context, and so you don't understand the consequences of your actions. Public access, now and in the future, to both private and public institutions, are threatened by the actions of IMSLP. The equation doesn't change just because you don't believe it's right.