What do you mean it’s far more complex?
Simply someone being accused of a crime isn’t enough to make them a public figure.
A public figure is one who had assumed a role of special prominence in the affairs of a society or thrust themselves into the forefront of particular public controversies. It can also be involuntary if someone has gained fame or notoriety.
So in same cases the media can create a public figure through their reporting and then be covered by the protection of NY Times v. Sullivan.
Gertz v. Welsh, 418 U.S. 323 (1974) and Dameron v. Washington Magazine, Inc., 575 F. Supp. 1575 (D.D.C. 1983) have more information on the public figure doctrine.