Is this translation accurate?

Some explanatory books, such as Nayl al-Awtar by Imam al-Shawkani, Mirqat al-Mafatih by al-Mulla Ali al-Qari, and the explanation of al-Mishkat by al-Tibi, have interpreted the hadith of Safiyyah (radi Allahu 'anha), when she said that the Prophet (salla Allahu 'alayhi wa sallam) "bana biha", to mean that he built a new tent because of her or with her. Is it valid to interpret the hadith of Aisha (radi Allahu 'anha): "bana bi Rasul Allah", to mean that he built a tent because of her or with her? My question is: is this interpretation acceptable from the perspective of the Arabic language?