The main basis for it is that the last part of the name Jerusalem is Salem, a detail not even obscured in transliteration. But it may simply be another example of a new city being named after an older one. And Jerusalem was not named that till the time of David, any verses in Joshua or Judges using the name Jerusalem are simply editorial additions from later on.
The Wikipedia page uses as evidence against the Temple Mount being the Mt Moriah of Genesis 22 the assumption that the Salem reference proved Jerusalem was already a city then. To me the evidence of that being Moriah is far stronger then Salem being Jerusalem.
Psalm 76:2 is usually considered verification of it being Jerusalem. First of all Salem as a shortening of Jerusalem being used for that city during or after David's time doesn't necessarily prove where Salem of Abraham's time was.
However on top of that. Psalm 76 seems to have an eschatological aspect to it, either the Millennium and/or New Heaven and New Earth. In which case it should perhaps be read in light of Ezekiel 40-48, where The Temple is not within the city limits of Yahweh-Shammah ("The LORD is there") but many miles north of it.
"In Salem also is his tabernacle, and his dwelling place in Zion."It could be that Zion here like in Psalm 48 is New Jerusalem, and Salem is where Ezekiel's Temple is.
One theory some have proposed for the location of Ezekiel's Temple based on how far north it is of the City is in the vicinity of Shechem and Mt Gerizim.
In Genesis 12:6 that area is where Abraham built his first Altar to God, and then traveled south to Beth-El, and then further south till the Famine brought him to Egypt.
At the end of Genesis 33 Jacob comes to this same region after making peace with Esau. There we are told in verse 18.
"And Jacob came to Shalem, a city of Shechem, which is in the land of Canaan, when he came from Padanaram; and pitched his tent before the city."Shalem is rendered differently in the KJV, and the Strongs also tries to treat it as separate (Strong# 8003 rather then 8004). But in the Hebrew texts it is identical to the name of Salem in Genesis 24 and Psalm 76 (three Hebrew letters, S-L-M). I believe it is the same city.
I feel like adding that any time we see the name Shechem used of this region or it's inhabitants (Shechemites) before or during Genesis 34 is an editorial decision from Moses much later. I feel Shechem became the name for this city/region from the person named Shechem in Genesis 34. I think the city of Salem and Shechem could very well be the same. But if not they are certainly near each other.
I think maybe Melchizedek became Priest of the Altar to God Abraham built in that region after he left it to travel south.
But there is also a city in the region known in New Testament and modern times as Salim near Nablus. John 3:23 says John was Baptizing in this region for part of his ministry at least. (I'm convinced however he must have been in the Trans-Jordan (Perea) region when he was arrested, since Antipas only had authority on the other side of The Jordan river.) This Salim was near Aenon which is affiliated with Mt Ebal.
Jerome stated that the Salem of Melchizedek was not Jerusalem, but a town eight Roman miles south of Scythopolis, and gives its then name as Salumias, and identifies it with the Salem where John baptized.
However there are also those who calculate Shiloh to be the site of Ezekiel's Temple.
Shiloh is close enough to the later city of Shechem that it could be defined as the same basic region.
Actually the name of Shiloh derives from the same root word meaning Peace that Salem does (Strong number 7951).
References to the city of Shiloh don't start till the time of Joshua, long after the references to Salem in historical contexts ended.
Shiloh is where the Ark was throughout the Judges period, close to 450 years.