Sony apparently plays several roles, of which I am not clear. But I think it’s no different for a library than individuals because I dropped off a bunch of DVDs at my library as a donation, and they simply took them to lend out. This implies there is no complex arrangement for libraries.. in which case I suppose Sony’s royalties are fixed and paid when the disc is purchased. So, I’ll not worry about feeding Sony by the mere act of borrowing a blu-ray. Though I will still favor DVDs when available so as to signal to the library a higher demand for DVDs than blu-rays.
I also recall some musicians saying they are okay with the library lending out their music because they want to support the concept of public libraries. It probably would not have even been up for discussion if they were getting any kind of compensation per rental.