I'm a bit late to this whole "Axl's voice on recordings-party" but this is how I see it!
When you're there in person, there's so much going on, the excitement is huge, one of your favorite band is up there playing some of your favorite songs and you just enjoy it, you don't analyze it in the same way as you do when watching a periscope stream. A personal example of this was when I saw Slash with Myles in 2015 I thought that the SCOM solo was the best live performance of that solo ever, in fact I updated YouTube like every 5 minutes on the train ride home just to hear it again but when a video of the song from my gig finally got uploaded it was on par if not even worse than most other SCOM solos Slash has played over the years.
And I am also of the opinion that you don't really notice Axl's vocals as much in person since it isn't THAT bad (take Paul Stanley for example, you'll probably notice his bad vocals a lot more in person since it is in many cases a lot worse than Axl's), you might notice it on YCBM for example but overall you most likely will not do that on most songs. What you however will notice is the things that is really good, the LALD and WTTJ screams etc. and that will then color ones opinion on the over all performance.
But as I said that's just my take on it, the theory that phones don't pick up his actual voice is just stupid. What phones don't record is the experience and the excitement, but they do record Axl's voice.