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Ok, so let me tell the story.

I wanted to have a 5IV Aegislash, and I had a 5IV Pachirisu, so I thought, hey, I'll just get a Snorunt from the Friend Safari and breed them. So I go to the safari, and the very first Snorunt I caught had 4 IVs. I had the wifi off (so my friend being online couldn't have affected this), so I couldn't figure out how it happened. I assumed I just got really lucky and moved on.

Then things got really weird when I bred a 3IV Snorunt (Everstone) with a 5IV Honedge (Destiny Knot) and got a 6IV Honedge on like the 10th try. I don't know the exact probability of this, but I'm positive the chances of this happening are very, very slim.

So my question is, did I just get really, really lucky or is there something else behind this?

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wait, what does having a 5 IV pachirisu have anything to do with your question?
He said he got a 5 iv pachirisu then he thought he can get a 5 iv snorunt from the safari too
oh, ok

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I am pretty sure you just got extremely lucky.
Also Pokemon found in friend safari's have atleast two perfect IVs guranteed
And seeing as you had an 5 IV honedge and 3 IV snorunt lets just assume that hone edge got perfect IVs only from both parents and the final Stat was randomly decided

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Yes, this is what I thought happened.  But crazy, isn't it?