No one is really denying that "Iran" is involved. The question is "who" in Iran is involved and in what capacity?
This could go many ways. Corruption and little fiefdoms and such are rampant in the Middle East. Militias a good example. Alcohol (like Lebanese whiskey, beer, and Russian vodka) is commonly smuggled through Iraq to Iran. Opium and Heroin at times travels in the other direction on it's way to Europe.
In Iran you have to consider the intentions of it's government, it's religious leadership (a parallel government in it's own right), and the intelligence branches (which seems to be it's own shadowy power base, much like the one in Pakistan).
The question is if the arms from Iran are sanctioned by their government? Or by the religious leaders? Possible? Yes. No proof presented as yet. Iraqi forces can be getting that equipment from the black market or unsanctioned rouge groups. Iranian police and intelligence agencies may be well aware of the conduit these arms and munitions are getting to Iraq though, and chose to look the other way.
Iran is certainly providing monetary funds to Iraqi Shiis groups, which would facilitate them purchasing arms over the black market, which incidentally come from Iran among other sources.
Sorry, nothing in the Middle East is ever simple or straight forward.
And if they are, what course does the U.S. take? Openly confront Iran? Simple enough for Iran to restrict oil flow out of the Persian Gulf.... thus creating world-wide economic panic. They quite literally may have us over a (oil) barrel. That is the fault of America... it's citizens, it's (lack of) leadership in government, and it's self-involved corporate leaders.
Pick your cliche: Sow the sky, reap the whirlwind. Time to pay the Piper. So long as the United States is dependent on oil from the Middle East, it will cost America heavily in terms of taxpayer money and the lives of it's soldiers.
You want it simple: Oil = gold + blood. That simple.