I am also wondering if you have more than one way that you are related to this fourth cousin once removed, through a first cousin marriage that so far you and your match are not aware of.
My paternal grandparents were first cousins, and this has made it much easier to find persons related to my paternal grandmother. In fact, my closest DNA match is a first cousin once removed in that side of the family; we share enough DNA that we appear to be first cousins.
My oddest DNA match (so far) is a half second cousin twice removed; her grandfather and I are half-second cousins (that is, we only share one great grandparent). This young lady (born 1991) and I (born 1959) share 110 cM across 4 segments, with the longest segment being 84 cM. It is amazing to me that this 84 cM segment has been passed down unchanged from the one ancestor that we share, Hyman Eliezer Lak, born about 1845 in Zagare, Lithuania.
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus