The reason is because there is writing, but if there is no writing; no - טעמא דאיכא כתב הא ליכא כתב לא
The גמרא assumed that שמואל maintains that it is a גט even if later he said it was just a נייר חלק. In the הו"א the גמרא assumed that she is מגורשת ודאי either because the בעל is always נאמן , or because it was actually read before they gave it to her, or because they viewed the גט from afar.
And שמואל also said, we are concerned - ושמואל נמי חיישינן קאמר
If one gives his wife a נייר חלק and says הרי זה גיטך there is a חשש גירושין, even if we did not examine it במיא דנרא. If however it was examined and no letters showed up, there is no חשש of גירושין.
The גט should be read by the ע"מ before the נתינה (and preferably after the נתינה), otherwise she may not remarry (unless it is read after the נתינה). [If the גט was not read at all there is a dispute whether אם נשאת תצא or not.]