I, too have this problem. I have a brand new (1 day old) Samsung Note 4. The way my old Samsung GS3 worked was that if wifi was on, the mobile data logo disappeared. It was clear that I was not using mobile data. (This was also on Sprint).
Now on Verizon with a brand new device, I noticed that the mobile data 4G logo stays on even when the wifi signal is active. The mobile data transfer arrows sometimes appear, again even when wifi is turned on.
To fix this, I first turned off the Smart Network Switch to keep wifi as the data transfer method. It seems to work most of the time, but the 4G logo is not greyed out, and occasionally the mobile data transfer arrows light up, sometimes even when wifi data is being downloaded.
I now have to completely turn off mobile data while I am in wifi range, just to make sure I am not accruing mobile data usage. I understand that there are some apps that use mobile data (such as texts), however, despite not being a big sender of texts, the mobile data arrows seem to light up randomly. The Galaxy GS3 never had this problem.