The story is contradictory in other ways.
You can’t both argue that the Israelites did their exodus from Egypt AND Saudi Arabia and that both countries are trying to cover up evidence of it.
Nobody is arguing that.
The Exodus took place from Egypt, into 'The Wilderness'.
The Israelites then spent considerable time encamped at the foot of 'The Mountain of God' before beginning 'The Wanderings'.
That is where Moses received the tablets; and where the Tabernacle, Altar, Ark, and all the rest of the items for the worship service were made. It is also where Aaron & his son's were consecrated as priests...and where two of Aaron's sons were struck down by God for offering 'strange fire' to Him.
It is arguing that the mountain is in northern Saudi Arabia, rather than the traditional, relatively nearby, site of Mount Sinai on the Sinai Peninsula.
The Gulf of Aqaba (Eilat) is that long, skinny finger of water the juts off to the NE from the Red Sea, (a drowned portion of the Great Rift) and separates the Sinai Peninsula from Arabia.
You can’t both argue that the Israelites did their exodus from Egypt AND Saudi Arabia and that both countries are trying to cover up evidence of it.
This is an understandable impression because of the author's sloppy and misleading writing style, wherein she wrote "One reason may be that the explorers have discovered a mountain on which are located the remains of religious altars, ancient Semitic inscriptions, and evidence of major encampments by nomads at the base of the mountain—all of which are elements, of course, of the Biblical narrative of the Revelation at Sinai. If the Exodus really took place in northern Saudi Arabia as Mr. Mahoney and his interviewees maintain, then the Arab claim to be the sole "indigenous" inhabitants even of the Arabian Peninsula itself, let alone "Palestine," could be thrown into doubt.
What she has done with her careless writing is to muddle the distinction between the point of origin of the Exodus and the subsequent route of the Exodus. What she should have said was "If the route of the Exodus took them through northern Saudi Arabia..."
I haven't seen the movie on which the article is based, but I'm certain it clearly differentiates the two. There is no scholarly dispute that I'm aware of that the Exodus originated FROM Egypt, but there are several competing theories as to the actual routes which might have been taken by the Hebrews on that long journey. One can do a lot of wandering in forty years.
Re: “from Saudi Arabia”???
The article says the Jews left from Egypt TO Saudi Arabia instead of the Sinai.
This section that you mention was poorly worded. I am not sure if you are familiar with the book of Exodus, but the story starts in Egypt, moves out of Egypt to Sinai / Northwest Arabia, then back to Egypt, then back to Sinai / Northwest Arabia. The reason I typed Sinai / Northern Arabia is that is where the debate is. Did the Israelites move to Sinai or to Northwest Arabia. This is a big debate between those that believe in a literal Exodus. So the Exodus was from Egypt, but moves to one of the two other areas.