That's an assumption made by a GC holder who had his/her parents' visa applications rejected. Similarly, you could end up meeting a student who might opine that its tougher for f-1 visa holders to invite their parents because s/he had his/her parents' applications rejected.

It's all subjective as everyone's case is different.

Besides, one could tell that you're a Permanent resident and you're already set to apply for their visas (if you haven't already). Maybe you should work on getting proper documentation.