Can an Amora argue with a Tanna?
From the Talmud it would seem that an Amora cannot argue with a Tanna and that is why it tries to fit in all Amoraic statements into the words of the Tannaim.
No. This is a commonly stated rule post-Talmud, but it is also simply accepted without debate in the Talmud. One example is Gitten 49b-50a where Mar Zutra makes a statement that when the Mishna says that when land is foreclosed on to collect a Kesuba the land taken from the least valuable-per-acre land (Ziburis) it is only referring to if the husband dies and she is collecting from the heirs. If, however, he divorced her and she is collecting from his property, she gets the mid-valuable land (Beinonis).
The Talmud goes back and forth on various potential Braisos which potentially contradict this, and finally Ravina concludes with a Briasa which unambigiously does, thus Mar Zutra's opinion is rejected.
This is one of many examples where when a Tanna is found to have said something in contradiction, the Amora's opinion becomes inoperative.
Rabbi Steinzaltz discusses this rule - and parenthetically gives the reason that Tannaim had access to reliable Mesorah that the Amoraim didn't - and notes a quazi in-between exception, that of Rav, who was the first generation Amora. He can be found to argue and be quoted in non-codified Tannaic statements (Briasa), but the Geonim explain that he could not even potentially argue with a Mishna.
The Meiri writes in his introduction to Avot that actually Amoraim sometimes do (rarely) argue on Tannaim:
ונמצא מכל מקום שהמשנה היא סידור רבינו הקדוש והברייתא עיקרה מר"ח ... ועם כל זה נתמעטו הלבבות מרוב הצרות והוצרכו האחרונים לחבר אחריו דרך ביאור והרחבה ולפעמים דרך סתירה ותיקון כשהיו חכמי הדור מסכימים לכך ממה שרואים בו קושיא חזקה
Thus, the Mishna is the arrangement of Rabbenu HaKadosh, and the Berayta is mostly from R. Hiyya...Nevertheless mental acuity decreased on account of the travails, and the later [generations] (i.e. the Amoraim) needed to subsequently compose [works] as explanations and elaborations, and sometimes in contradiction and as corrections, when the elders of the authorities of the generations agreed to this, on the basis of strong questions that they found.