Is it ok to ask my supervisor about a coworker's FB photo that I "shared"?

[innocent but deadly]

My coworker posted a photo on FB about a blue pill called Fukitol. It's pronounced Fvck it all, and ppl take it when their life sucks. I shared it on my timeline bc it was funny. The next day, a friend told me she'd get notified that I shared her photo. I panicked. She and I weren't friends on facebook and didn't even know I had a facebook. She didn't think I knew she had FB either. I figured she would hate me for intruding on her profile like that. When I worked that weekend, I ran this by my supervisor and asked her if my coworker would hate me. After telling me no that girl ain't gonna hate me and why she wouldn't, my supervisor asked me why I shared that with her. Now I'm confused. Don't companies have open door policies where workers share work related concerns? If this involved a coworker, doesn't that make it work related?

Did she react that way bc I accidentally said "Fvck it all" to her when I referred to that pill? And I said the word, not the letter.