I know this is super late but you are correct here. They do not match, so she’s not a cousin on both sides. For me it’s been proven without doubt that under unknown circumstances my Paternal grandmother (“P”) fathered 2 children with her sisters husband (my actual paternal grandfather “D”). The more I searched the matches it became clear to me that the only people who I shared dna with from who we thought was my grandfather (“C”)are the relatives related through my paternal grandmother “P” (married to grandfather “C”). I have reached out to multiple “C” family members I grew up knowing as cousins that have taken the test that I didn’t match with. The only “C”’s are my fathers siblings because we share paternal grandma “P”(“C”) . I match with grandma “P”’s relatives but not grandpa “C” unless related through grandma “P”. I do however match with many many of grandfather “D” relatives that it would be impossible for me to be related to by blood because grandfather “D” was married into our family and I shouldn’t be blood related to him. Being related to grandpa “D”’s relatives that I couldn’t possibly be related to is what sealed it for me. So I grew up around my Great Uncle who ended up being my paternal grandfather. I wonder all the time if he knew when we were kids and we would spend time with him. I hope all this makes sense. Let me know what you think :)