Redleg, it is prohibited to do anything thàt’ll result in romantic feelings. As such it is impermissible for a man and a woman to have a close friendly relationship.
Regarding Rav Moshe, what he paskens is that it is prohibited for a male and female to be friends. No one disputes this halacha. The only machlokes is whether the prohibition is a m`doraia or whether it is “only” a severe rabbinic prohibition. No one at all disputes that it is prohibited.