Actually when you think about it. TrainerRoad has the data to help answer this.
They have a bell curve, so they could show us how much rest the top athletes take by plotting that alongside.
It wouldn’t be conclusive as they can’t see everything an athletes does, but they do have access to a full Strava sync.
What they could do is analyze how many TR athletes adhere to the rest week’s and whether or not they follow the prescribed workouts or deviate/skip/etc. I don’t know if they could conclude whether or not there was any physiological benefit, but it would be interesting to see adherence (or not) to plan.
My guess is that a fair number of TR users don’t execute the prescribed rest weeks.
Some people have an innate sense of how much they can do, when to back off, and when to rest. Others need it spelling out in a plan set out for them or a coach saying take a break.
Some get injured almost every year some go decades between any hint of injury. Which category does your friend fall into?
8 years ago I used to ride most if not every day; factoring in a very easy recovery day and cooldown after harder rides and it seemed to work for me (injury free) then again I was in my late 30s. I’m in my mid 40s now and still injury free but factoring in my rest days I seem to be just as quick makes me wonder if I had took more rest days when I was younger. Then again it was good for my mental health riding every day 
I know more than one person that has a hard time noodling along on their bike at a low level of effort. I believe in that and can mindset it, but at times I really have to discipline myself to keep things in check. I don’t usually wear team kit on those days. One thing that has helped me greatly in this regard is to basically kiss Strava goodbye. I am now very choosy about chasing Strava segments.
So far this training season (I started back in September) I take “recovery” rides only when my HRV app suggests it and I have an off day and then it is something like Dans or Taku-1. During outdoor season I’ll take an easy 30 minute ride around usually early in the morning to catch the early morning sun.
It is week six of SSBLV for me and I’m doing the workouts in 3 consecutive days so I can take the rest of the week totally off and get away for my first, last, and only ski trip of this winter.
You can increase rest from 2 to 30 using the following sequence:
Up-up-down-down-left-right-left-right-B-A-B-A-Start.
Don’t know about any study but I would say that on the long term it’s about playing it safe and taking that weekly rest day.
You could turn one day into a double day freeing up space for a full recovery day and get in even more volume. For example: finish off week with a long ride on Sunday, take Monday off and double day on Tuesday.
In the long haul the full rest day will pay off.
Gold! 
I prefer the magic turtle shell method.
Or, is it a tortoise?
Beyond physiology, regularly scheduled full rest days help because they’re a mental break for some. Personally, I’ve found WAY more consistency in the last five or six seasons where I always schedule Sunday off to sleep in, play with the kids, and spend time with the family. For a long time when I was single, I trained 7 days a week, and usually three of those were two-a-days as a multisport athlete. After about six months of that, I needed mental breaks, and I struggled to want to get back into it after A events.
Since implementing scheduled rest days as a triathlete and now just cycling, I can’t remember the last time I lacked for motivation… it’s been literally years and I have to force myself to take my transition downtime in the late fall. (And, FWIW, my FTP is 30W higher than it was before I became a daddy four years ago thanks in large part to consistency.)
Sometimes holding yourself back just a little bit is the best thing you can do long term.