As far as "five miles," I clearly stated in my second post that I simplified "controlled airspace" by substituting "five miles", as most understand the generic five mile rule, which generally implies controlled airspace to-the-surface to the layperson. To debate that point further is merely being pedantic.
On the recreational issue, it DOES make a difference, because in the above scenario one person stated that the "tower" told him he does not need to call in if flying below 150'. Someone else in the tower may have another opinion. If the pilot has an incident within five miles, but didn't call in because "someone" in the tower once told him he didn't have to, he would potentially be in violation of the notification rule.
And for authorization versus waiver, the FAA informs us, "If you can comply with all of part 107 (without needing a waiver), but need to operate within certain controlled airspace (Class B, C, D, or E surface area), then only request airspace authorization, per section 107.41.” So, are you saying you personally have successfully used a waiver to obtain permission to fly in controlled airspace for long durations like a week, month, year?
You're trying to split hairs and it's pointless to try and convince you otherwise.
In regards to "So, are you saying you personally have successfully used a waiver to obtain permission to fly in controlled airspace for long durations like a week, month, year?"
No I personally have not because I've not requested such. I have professional colleagues who have and more are approved every single day. Spend some time and do some reading and you'll see Airspace Waivers are a REAL thing.