As correctly noted by Joe Black, most scholars consider the mention of Philistines interacting with Abraham to be an anachronism. WHY? Abraham is dated circa 2000 BC according to some scholars, there is NO evidence of Aegean peoples at Beersheba for that period of time. There was found debris from the Chalcolithic Age (Stone Age) but that is too early to be Abraham's world. Beersheba and its well are dated to the end of the 12th century BC or beginning of the 11th century BC by archaeologists. Hence, some would argue Abraham is in reality a fictional character of the 12th/11th centuries BC when Philistines were in the area, they having arrived from the Aegean World (Cyprus) by 1175 BC to settle in Canaan. It was the presence of Philistine pottery sherds in Beersheba's earliest stratum IX, that dated the founding of Beersheba, for the archaeologists. So, the Bible has Beersheba being founded by Abraham in a Philistine world, and archaeology has confirmed that Beersheba (modern Tel es Saba) was indeed founded in a Philistine world of the late 12th century BC.
I know professor Aren Maeir doesn't give much credence to the inscription found in terms of identification of the locals. He feels it has to do more with trade than immigration.