Adopted from the book : "Fadak in History" by : "Shahid Muhammad Baqir as-Sadr"
Some of those,who defended Abu Bakr concerning the matter of Fadak,mentioned that Imam Ali did not recorver Fadak and he left it for the Muslims following the same way of Abu Bakr, so if Imam Ali knew that Fatima's allegation (of Fadak) was true, he would not do that!
I do not want to wide-open,in this answer, the door of taqiyya1 and to try to find an excuse for Imam Ali's doing,but I never believe that Imam Ali had followed the way of Abu Bakr.History did not show anything of that,but in fact it showed that Imam Ali thought that Fadak was the prophet's heirs'. Imam Ali recordered this clearly in his letter to Othman bin Hunayf2 as you will see ain a next chapter.
Perhaps Imam Ali intended that the yields of Fadak concerned Fatima and her heirs, who were her children and husband, and so the news did not need to be spread because Fadak was in its legal possessors' hands,who were him and his children's content3 or they might dedicate it and made it as charity.
1- To hide one's true beliefs when life is in danger.
2- Sharh Nahjul Balagha by ibn Abul Hadeed,vol. 16 p.208.
3- This was the most acceptable possiblity because the first was rejected by the letter of Imam Ali to Othman bin Hunayf when he said: and others withheld themselves from it ..." and the third was rejected by the acceptance of Fadak by the Fatimites.