The Baelish we saw die wasn't the real Baelish, it was a faceless man in his place.
Also, Baelish's sigil is a mocking bird.
"Both male and female mockingbirds sing. They often mimic the sounds of birds (and frogs) around them, including shrikes, blackbirds, orioles, killdeer, jays, hawks, and many others. They go on learning new sounds throughout their lives. "
So they mimic those around them just like how the faceless men masquerade as other people.
"a man with no motive is a man no one suspects, IF THEY DON'T KNOW WHO YOU ARE, or what you want, they can't know what you plan to do next".
There are so many fucking hints that he's either a faceless man or intricately connected to them in some way that anyone that thinks this theory is retarded is a complete fucking moron.