You are spouting nonsense. With the exception of competitive residencies like ortho, derm, surg etc, most programs are within reach for IMGs.

I myself am a Singapore who went to a third tier med school (SGU in the Caribbean) and I managed to match into Tier 1 Psych program at Emory. Most of my classmates also matched into residency of their choice, although many went into FM/IM/Peds..