I found some related questions about this, yet no answer.
Using a freshly bought "5V/2.1A" rated power supply, I get undervoltage warning icon on both my Raspberry Pi 3s. I measure 4.75V at the USB ports.
I feel like this should not be happening.
The APX803 chip (which monitors voltage) triggers at 4.63±0.07V.
This is an instantaneous level, whereas your meter will show average. Even assuming your meter is correctly calibrated the trigger may fire if the load varies. The visual trigger has a 3 sec so it will show even if the average is 4.75V (which is already at the lower end of the tolerance range).
The Pi3 actually has a well engineered power circuit, and the SOC will continue to function even if the input voltage is below spec. The same may not be true of the peripherals.
The addition of WiFi and Bluetooth, as well as the faster processor means the Pi3 is more prone to these issues than the Pi2.
Unfortunately the Pi cannot compensate for inadequate power supplies. There are very many of these - I have a few myself, although not as bad as 4.75V.
If you use a cable to connect your PSU to the Pi (if it does not have an integrated lead) you may want to try different leads. Many of the cheaper cables have excessive voltage drop - I actually make my own with decent sized wire.
One of the major causes of problem is high powered peripherals e.g. HDD etc. I suggest you use an external hub if you use these (as do most of us).
It is actually quite simple to design a PSU which would meet the Pi spec, but I couldn't do it for less than $20 which most of the commercial units do. These are really designed to charge smartphones, which they do adequately.
I have tested a number of PSU (with a dummy load) and have yet to find one which actually delivers the rated voltage at the rated current.
I would suggest that your power supply is the problem. I had exactly the same issue on my Pi 3 with a power supply I sourced on Ebay rated at 2.1A/5V, I tried an official 2.5A/5.1V supply and all my problems went away: Official RPi power supply
This article claims the minimum voltage requirement to be 4.8V: RPi Minimum Voltage
Indeed, this problem is, 9 times out of 10, the cable. Even when you may think it can't be.
I recently tacked this issue with a very good power supply (12V, 2A) through a 3A 5V switching regulator, which was fed into the Pi using 8 inches of somewhat inferior USB cable. Constantly giving under-voltage warnings.
However, trim those 8 inches down to just 2 inches of inferior cable (all I wanted it for was the plug) and magically the warnings vanished. Gone. Nada.
You wouldn't think that just 6 inches would make any difference... but the Pi3B+ is just so sensitive (overly sensitive if you ask me... I *don't * need to know if the supply has dropped out for 23 picoseconds) it borders on paranoia.
Try to use another cable in order to connect your power supply to your Raspberry Pi. Thin and long cables result in high voltage drops over the cable because of the high current. In my case, this caused the undervoltage warning. I ended up cutting a thick USB extension cable shortly after the USB plug and connecting it directly to the Pi's GPIOs. Now, everything works fine.
I assume you're referencing this question from the official Raspberry Pi Foundation's forum. If you look at the post again, you'll notice that the post was written in 2014. Your question states that you're using a Raspberry Pi 3 which was released in 2016.
I haven't been able to find a more recent posting from the foundation, but one could simply assume that the warning is displayed at a different threshold for the RPi 3. Since the RPi 3 requires significantly more power, it makes sense that it would have a tighter tolerance.
My Pi 3b runs off a 7.2Volt 3600mA NiMh Rc-car powerpack. With a MB102 breadboard power supply module that can take from 6.5 to 12 Volts input and outputs 3.5/5 volts. I have no under voltage warnings.