I like a word you suggested, true.
She received a true degree in 1999.
Although I don't know if that is making a strong statement than the simpler:
She received a degree in 1999.
If you represent the university, then perhaps
We confirm (authenticate) that she received a degree in 1999.
As to the second part of your question, establish is a fine word to use, as in
UNC established the Mathematical Finance graduate degree in 2002.
You might also say,
UNC first conferred the Mathematical Finance graduate degree in 2004.
If the emphasis is on what a third-party has established about the program, then you might say,
The M.A. in Counseling was accredited in 2006.
If these answers don't suffice, then perhaps the beta site, academics.stackexchange.com, might be of help.