I made "custom" mobs by adding player_heads with curse of binding to mobs. These mobs will replace the player_head with even a leather_helmet if it encounters one... breaking the illusion it is a custom mob.
How to reproduce
/summon husk ~ ~ ~ {CanPickUpLoot:1b,ArmorItems:[{},{},{},{id:leather_helmet,Count:1b,tag:{Enchantments:[{id:"minecraft:binding_curse",lvl:1s}]}}]}
/summon husk ~ ~ ~ {CanPickUpLoot:1b,ArmorItems:[{},{},{},{id:player_head,Count:1b,tag:{Enchantments:[{id:"minecraft:binding_curse",lvl:1s}]}}]}
Throw a diamond helmet at both husks; the second one will pick it up, replacing its item.
Linked issues
Comments

I'm also unable to reproduce in the current version.

Shouldn't the resolution be "Fixed Version 1.16.2", as it was reproducible in 1.15?
We don't know for sure when it's been fixed. Could have been in 1.16 or 1.16.1. Even if it was fixed in 1.16.2, which snapshot did? For documentation purposes, it's better to close as cannot reproduce in these cases.
I am no longer able to reproduce in 1.16.2