Coworker [25F] thinks we [22F] [20 - 30 F/M] are using "office politics" to bully her?

I've been a high school girl, so I know bullying in the form of ostracization. But this is not the case. There are no "office politics" oppressing the victim.

More or less, everyone in our office became close knit about 3 months ago. We were all in the same training class for a new branch in our company. After finishing training, majority of the people in the office felt comfortable exchanging Facebook info.

One person, Kathy [25F], told us all she didn't use Facebook. This was a lie because I had searched her name and found her before she stated this. It was an active and very public account, but I never outted her to the rest of the group. I believed it was her nice way of turning us down. I understood because not everyone is comfortable with work friends on their personal media.

Some weeks past and she lets it slip that she has a Facebook. Something about her dislike about her friends sharing stuff on her Feed. She was called out and she admitted she just didn't want to mix business with pleasure. Kathy didn't want work to get mixed with her personal life. Again, we understand.

So more months passed. And during said months, our group interacted outside of work. We went shopping together, had BBQ, movie nights, drank wine and watched Scandal, etc. And with this came inside jokes, more invitations, and emotional connections (?)

Last Monday, Kathy complained to me that our coworkers Brad and Joey were having a laugh during break. She feeling left out, asked what was so funny. They said she just had to be there to get it. She asked them to say it anyway, and that she'd probably get it. They did through giggles and when Kathy didn't laugh, they repeated she just had to be there to get it. When Kathy repeated the joke for me, I burst out laughing because it was an inside joke about something that happened at Joey's movie night. Kathy seemed hurt and went back to her desk.

Today during break, Patrice asked our other coworker Nancy what she should bring to Scandal night. This exchange happened in front of me and Kathy. Again Kathy piped up and asked what they were talking about. They explained that a few of us coworkers were getting together to watch Scandal and drink wine. Girl talk and stuff. They then started a conversation about the latest episode.

Kathy pulled me to the side and asked if everyone was doing things without her. I told her yes. She asked why she wasn't invited and I explained that it was because she told us she didn't want to mix business with pleasure. She still insisted it was rude not to ask and they were using "office politics" to bully her. She ranted about how she feels victimized and ostracized when she isn't included.

How do I explain it to her that her not being included is her fault and she can't force people to like/invite her?

TL;DR: Coworker doesn't want to mix personal life with work. She gets annoyed when everyone seems closer and does things outside of work without her.

EDIT: Bolded for emphasis since there is some confusion. Kathy has stated she doesn't want coworker interaction outside of work. Not just Facebook.

Ever since Kathy found out everyone does interact outside of work, she's been very curious about my texting (on break or after work). She wants to know if I'm texting X coworker or doing to X's coworker's event.

UPDATE (is this how I do it?):

I talked my coworkers during our time before shift starts (usually a coffee and donuts thing for everyone). I phrased it so that it seemed like I was hurt by the group talking about Scandal night in front of me. They understood and promised to keep that to themselves. I also stated that maybe next time me and Kathy could go.

Nancy was confused and Brad was visually disagreeing/pissed. Apparently, Kathy lied to me about not being invited. Why, I don't know.

Nancy sent Kathy a FB message weeks ago. Nancy said that she was thinking about having a TV and wine night. She listed a few shows and asked Kathy which would like to watch. It took Kathy a few days to respond after reading it. In the response, she said she “had better things to do then drink cheap wine and watch trash tv.”. Also to not message her on FB again. I physically saw the message to confirm it wasn’t some fake screenshot. I asked Nancy why she didn’t tell us about this and she said it would make the workplace hostile.

Brad also noted Kathy was a bitch and that I should just check out her Facebook. So I did and like before it's a very active and public account. Apparently, for months she's been posting status (Kathy's Tea) about our workplace. Sometimes venting, sometimes actually harmful statements. One that really bothered Brad was when she took creepshots of everyone and posted that he was a fat N-word (hard r), something about Tyler Perry. He only found this out because one of Kathy's FB friends sent it to him.

I was also not left out as she posted a direct photo from my own social media and captioned it that I'm a bottle redhead who sets feminist back. There was something about Nancy's Scandal night, but she called it for desperate soccer moms and wannabe stepford wives.

Brad said he didn't want to tell us because he went to HR and they haven't gotten back to him yet. That they said though it counts as cyber bullying, it's her social media BUT she had her phone on the work floor (against the rules).

So now I have all this information and confused on what to do. Kathy's been lying to me and very rude herself. But why would she lie to me? What her end game?

I have about 4 hours until my break with Kathy. Should I confront her?