But does MLB own the rights to the stadium? They aren't the only ones that play there. The stadium I mentioned was also the home for the NFL team, plus college teams used it and it was used for 10+ years for the Army/Navy games.

According to the internet (and they never lie.. http://football.ballparks.com/NFL/PhiladelphiaEagles/) the stadium is/was owned by the City of Philadelphia.

Even Safeco field, the one that the original email is about, is owned by Washington-King County stadium authority with only about 20% financed by the Mariners themselves.