So, after further experimenting, I was finally able to hear the EMI noise everybody was talking about. However, it took some true effort to bring it up.
The noise was only present when the phone was in a very specific position from the Sparrow (using the stock short cables). I had the Sparrow connected to my MacBook Pro, so I had the flexibility to move the phone around the it. The noise/crackling was the most present when the phone screen was in direct contact with the Sparrow.
I mentioned that I used the Sparrow for over 5 months. Well, I didn't mention that the Sparrow was connected to my Mac with the standard TR-Amp cable — on which the EMI noise isn't present unless the screen is in direct contact with the Sparrow. The cable is unbranded and it is your standard black rubber cable. It has "E319028", "AWM" and "Style 2725" written on it, but I didn't get any clear result from searching any of those.
"Lab" testing and experimenting will be required from EarMen to make sure that nothing alike happens in the future