If one statically links ffmpeg into a larger proprietary application, the only source files one needs to supply are your ffmpeg sources, modified or not. The rest of the application's source does not have to be released. In my (now ex) employer's case, only the low level av_read_frame() function was modified. The entire ffmpeg version used, plus a notice about that being the only modification, is in the software as well as the employer's web site in multiple places. They're a US DOD contractor, so their legal team is pretty serious.
a) […] if the work is an executable linked with the Library, [accompany the work] with the complete machine-readable ‘work that uses the Library’, as object code and/or source code, so that the user can modify the Library and then relink to produce a modified executable containing the modified Library. […]
b) Use a suitable shared library mechanism for linking with the Library. A suitable mechanism is one that (1) uses at run time a copy of the library already present on the user's computer system, rather than copying library functions into the executable, and (2) will operate properly with a modified version of the library, if the user installs one, as long as the modified version is interface-compatible with the version that the work was made with.
