It's both. The lag is real for many people for a variety of reasons. As is exaggeration.
I play with one guy that complains every time he gets killed that he's being one shot by mida or doctrin but is equally untalented in pve.
Or another guy I play with from Canada who has a horrible connection (always red bars) but some times get tons of kills or sometimes can't kill or damage a damn thing.
He'll I have good Internet and can't do damage to other green bars all the time. It's a frigging roller coaster and it does get frustrating.
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Same experience here, before each match I pray to the latency gods.