Ibn `Aashoor, in his exegesis التحرير والتنوير, pages 10-17, discusses the difference between تفسير (exegesis) and تأويل (interpretation). Since the latter is the word used in 3:7, his arguments are relevant o this thread.
He makes an excellent point as he reports a narration by `Aa'isha, may God have been pleased with her, in which she says,
كان صلى الله عليه وسلم يقول في ركوعه سبحانك اللهم ربنا وبحمدك، اللهم اغفر لي يتأول القرآن
"He, PBUH, used to say in his bowings: Sanctified are You, God, our Lord and with praise for You - interpreting the Quran.
He says she was referring to the verse,
and clearly understood that interpreting it
meant taking it for its obvious meaning. Umar and Ibn `Abbaas, on the other hand, interpreted it to mean that the Prophet's Message has ended and that he was about to die.
A great point. It means that تأويل may sometimes mean the obvious meaning, but since God makes it clear in 3:7 that only He knows the true interpretation of many verses in the Quran which He described as "mutashaabih", her understanding of the verse does not fully define it.
And he seems to favor the idea that تأويل means arriving at an ultimate meaning that was intended but purposely kept hidden. He says this is the linguistic meaning of the word: returning a word to its first (أول), original meaning. He gives a cute example:
and comments that the clause "He brings out the living from the dead" may mean to cause an egg to hatch into a live chick, in which case that would be exegesis. Or, it could means to bring out the believer from a disbeliever!
IMHO, the matter is much simpler. تأويل is impossible for us humans. Only God has that knowledge and has chosen not to reveal it in this life. This is confirmed further by,