Near Easterners have foreign (non-Europid) admixture, but so have other populations. The problem is just that especially the slave trade altered the classic Arabic variant, which was Arabid.
This Arabid is a clearly Europid variant and can be called Mediterranoid, but never Mediterranid. They are the "desert type" of the Southern Europid spectrum, simple as that and can be mainly distinguished from Mediterranids by their facial features and craniological details.
In v. Eickstedts work Iranids being the second subtype after Arabid of Orientalids, and Iranids (Irano-Afghans) are a clearly Europid form close not just to Arabids, but to Mediterranid, Nordoid and Indid the same time (the Aurignacoid spectrum of the East).
Nordindids are even classic Europids, Indid proper (Gracilindid) is a rather tropical adaptation of the Europid spectrum.
In fact Nordid, Mediterranid, Orientalid and Indid are to me, in a way, just different forms of the same basic theme, adaptations to the local climate of a similar basic (leptodolichomorphic/Aurignacoid) Europid form.
So it makes more sense to look at their habitat and way of life they lived in the times when they were formed rather than speaking about admixture alone.
The most Arabid regions of the Near East are, probably unfortunately, those which are now probably the most affected by Negroid admixture because of the slave trade. The "urban Armenid type" and Asian Alpinoid spread as well, especially in the cities and probably because of contraselective trends like elsewhere, so we deal with more complex mixtures in Arabic people of today.
Like I wrote in another thread about these two, clearly Europid/Caucasoid Arabids:
http://i19.tinypic.com/6gjeule.jpg
These two are two perfect Arabids who go somewhat, slightly in an Eastmediterranid direction even, like some Arabid variants do, others not - probably this is partly due to stronger-weaker Armenoid influences as well, though the classic Arabid morphology looks usually less "Mediterranid like" than these two. Clearly in the classic Europid spectrum and without visible non-Europid admixture.