Powering Neopixels and Arduino board from one adapter

I have connected a Neopixel ring to my Arduino board. Both have a separate power supply because the Neopixels draw more than 0.5 ampere (the maximum you can draw from the Arduino)

Now my project has two power inputs and needs two wall outlets, which seems rather clunky.
I found this circuit on Google that solves the problem and uses one single adapter to power both the Arduino and the Neopixels.

My question: can you apply 5V directly to the 5V pin on the arduino like this? Why not the VIN pin? Won't you fry your board like this?

If the adapter is a well regulated 5 volts then OK. However most low cost adapters are not that well regulated. So there is a chance that you will put more then 5 volts to the Arduino, that will fry it.

Vin provides power to the input side the voltage regulator which regulates the voltage from the Vin pin down to 5volts on the output side which is also connected to the 5v pin. Vin and the barrel plug are basically the same and require 7-12volts. To run the v.reg. The notable exception is that there is a protection diode connected between Vin and the plug. So the barrel plug has reverse polarity protection, but Vin does not because it is after the diode.