NOTE: I re-watched the perk system video and it doesn't really leave any room whatsoever for this speculation. So that makes the following largely pointless.
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At first, I was skeptical of the "perk-ception" statement, thinking it was lackluster reporting failing to phrase something correctly - again.
However, that statement comes directly from Pete Hines: http://gamerant.com/fallout-4-275-separate-level-perks-816/
I have a theory and what I'm kind of hoping is how the perk/skill merger works: Perks allow us to do something; the individual XP level for the perk governs how effective it is. For example, some people are really unhappy with the Wasteland Whisperer perk, but what if the first rank gives a chance off the bat that the animal is pacified and as you gain XP levels in that perk specifically by using it, the chance increases (to what I would hope would be a guarantee)?
Another example: Science! A given rank might increase your damage with energy weapons by 20%. Then, by using energy weapons, the XP rank for the perk increases which increases the effectiveness of the perk in turn (more damage). However, you have to have the perk first in order for it to start gaining XP levels (hoping that was obvious). Someone without the perk wouldn't gain any long-term benefit from using energy weapons.
This would mean instant gratification for taking a perk, but provide an incentive for repeatedly using it.
One last example for a perk that's a bit more...intangible: Strong Back. Roughly speaking, rank 1 increases your carry weight by 50 pounds, then there's other ranks for allowing you to fast travel when over-encumbered or run/sprint when over-encumbered (I believe, even if there isn't let's just say there is for this example). Rank 1 (carry more weight) allows you to gain XP levels for Strong Back at a very slow rate by carrying around stuff (keep in mind speculation here). The more weight, the faster you gain perk XP. However, fast traveling while over-encumbered gives you perk XP at a faster rate, and running and sprinting when over-encumbered gives you perk XP at an even faster rate.
Just the random speculation of the day