It wasn't heavily influenced...it WAS wing Chun he just put his own name on it. Taky kimura and James demile have both said in interviews it was wing Chun they were learning and they were some of his first students and back then lee didn't know any other styles so it was all wing Chun and only later did he start adding boxing and other stuff
He said he taught Jun Fan Gung Fu, he school was called the Jun Fan Gung Fu Institute. He wanted to further his Martial Arts training and gradually incorporate other techniques into it which would later become Jeet Kune Do. I don't understand people's problem with this method. I much prefer this approach opposed to schools marketing themselves as one style when there are hardly any elements of said style in their curriculum.
In FMA, instructors will change there system's name even if there's a shift on emphasis. Meaning, there's not even much of a change in techniques, just focus.
Lee on the other hand heavily modified Wing Chun and incorporated many other styles into his own.