No that is not true, Iraq has always been a kind of a buffer state and ally against external pressure, even in sassanid era the Arabs of Iraq served as allies against Arabs of Levant who worked for Romans, so this is an old policy and part of traditional Iranian statecraft.
Imagine having no ally but an enemy in Iraq, like Saddam or ISIS, it's a disaster, then things like Iran-Iraq war or nomadic muzlim invasion of Iran will happen if we go back in time.
Many Arabs like Iran, especially now. We spend relatively low amount of money on our allies.