That isn't an indefensible claim, but the Ottoman Empire ruled the Middle east for centuries. What democratic tradition did it cultivate?
The Ottoman empire was, certainly towards the end, a European colonial empire. It was a particularly reactionary and poorly administered empire, but all colonial empires were reactionary and poorly administered when it came to the colonies.
Regardless, the Ottoman Empire actually made significant steps towards democratization towards the end of its rule.
From the mid-19th century onwards, each province of the Empire was given its own local assembly, with guaranteed representation for non-Muslim religious minorities and control over many local affairs. In the 1876, the Ottoman Empire briefly became a constitutional monarchy, but parliament was abolished two years later (following a disastrous defeat by the Russian Empire for which parliament was blamed). Parliament was reopened in 1908, with stronger constitutional protections, and from the next decade until its destruction the Ottoman Empire was a constitutional monarchy much like any European constitutional monarchy.
Did it foster a lasting democratic tradition? Nope, but no colonial empire really did.
Also, the situation in the Middle East right now isn't a question of "hegemony." I mean, it's played a role, certainly (see Iraq), but Iran and Saudi Arabia have been waging a cold war for ages. And part of it has to do with the religious divide (one's Sunni, one's Shia - I forget which is which).
It's a proxy war.
Saudi Arabia doesn't have a domestic arms industry. It barely has any domestic industry at all. Where do you think it gets all the tanks and modern aircraft from?
Saudi Arabia has an absolutely enormous public sector, mostly overseen by the extended royal family and employing the majority of the indigenous Saudi population (which is, admittedly, fairly small). How does it pay their salaries given, again, that there is no domestic industry and the population barely pays taxes?
The main source of revenue for the Saudi Government is the Saudi Arabian Oil Company, until very recently the largest corporation in the world by market capitalization. It was previously called the Saudi Arabian American Oil Company, because it used to be owned by American oil companies. The Saudi royal family gradually bought Saudi Aramco from those American companies in a kind of soft nationalization, but is still reliant on American expertise and technical assistance, mostly in the form of expatriate workers, as well as on numerous joint ventures with American companies. In return, Saudi Aramco provides a stable source of cheap oil to the West, and in particular to its American allies.
The US has enormous interest in Saudi Arabia (and to a lesser extent all of Arabia) because any significant change in the political situation there would threaten the oil companies on which US oil imports rely. That is why Saudi Arabia is a key US ally in the region. That is why it is equipped with so much American military hardware.
The situation in Iran is more complex. Iran's oil industry was once owned primarily by BP. Iran nationalized its oil industry after the revolution and effectively cut ties with western oil companies (see my point about Islamism having a proven history of standing up to foreign interests). Under US lead sanction regime against Iran, Iran is not allowed to export oil. However, Iran covertly exports huge amounts of oil to China, and has joint ventures with the CNPC. Because the Iranian regime is hostile to Western interests, it is increasingly becoming a key strategic partner for China (and to a lesser extent Russia). Iran is an observer nation in the SCO (the Chinese lead strategic alliance) has applied to join the SCO in the past, and will likely be accepted as a full member in the near future given Chinese support. There has also been some discussion of Iran joining the CSTO, which would be unprecedented for a state not part of the former Soviet Union and shows how close the ties between Iran and Russia are.
I notice you've also completely glossed over Syria, because Syria doesn't make any sense within your understanding of the situation. Syria is a secular Arab nationalist (Neo-Ba'athist) dictatorship based on ideological principles of pan-Arab unity and societally dominated by Alawites. They are entirely, entirely ideologically and religiously opposed to Iran, yet the two are important strategic allies. Why? Is it their timeless religious affiliation shining through. No, twelvers (the dominant religious group in Iran) historically do not consider Alawites to be Shias at all and the Syrian regime is aggressively secular and wholly uninterested in the Sunni-Shia conflict. It's because they're both opposed to Western interests and are both strategic allies of Russia.
China and Russia tend to frame their international role as anti-colonialist. They're not influencing these nations like the mean horrible West does, they're just helping weaker nations to resist Western hegemony. It's exactly the same thing though. Soft power is soft power.
Wait, are we talking about liberalism or neo-liberalism? Because one's about ideology, one's about economics, and I don't think the former can really be said to have "backers."
At this point, politically, they are the same thing.
And of course political liberalism has international backers. Why do you think George Bush spent so much time rambling about bringing freedom to Iraq. It just turns out that freedom means the freedom to support US interests and to vote for a government that will support US interests.
Most of Europe has no responsibility for that mess.
Does your car run on magic?