YesRSA-OAEP does not provide "plaintext integrity in addition to confidentiality". By the definition of PKE, anyone with the public key can encrypt whatever
plaintexts plaintexts they choose. In particular, encrypting "a symmetric session key
appended appended with a hash or eventually crc value for insuring integrity" doesn't help.
To To get integrity, there has to be [something thesomething [the honest party knows which the adversary doesn't know] or [something the[the honest party can do that the adversary can't do].