It is not true. Palestinians cannot purchase property or build in the 93% of Israel - land that was requisitioned by the Israeli State after 1948. So in effect they cannot live where they want. They cannot live in any of the kibbutzim built on land stolen from destroyed Palestinian villages and even in the 'mixed cities' like Haifa the Palestinian population is kept at 30%. Tel Aviv has a Palestinian population of 4%, and permission is always denied for them building even within Arab neighbourhoods like Ajami -land given either to religious settlers or for luxury Jewish only housing. In East Jerusalem, planning policy is racist, since the state plans to reduce an Arab majority population of 58% to 30% by ensuring the transfer out of Palestinians from Arab neighbourhoods surrounding Jerusalem. Within Israel, new housing communities are given the right, in every case to refuse admission to whomever they feel 'undesirable', in effect, 'keep Palestinians out'.
Palestinians are almost never given permission to build or extend their homes in the mixed cities, and thousands of homes, even within Israel, are scheduled for demolition, due to not being given permission, of for 'Judaisation policies. In the Negev,Bedouin villages are being demolished to be replaced by Jewish-only settlements built over them. Most Israelis, in polls taken, would not like to have Arabs for neighbours etc etc
For more, see Ben White's book, 'Israel Apartheid'.