If another person is going through something that calls for compassion--but they "reject" the compassion--it's most likely the delivery of it that is being rejected.
An example: A friend of mine (let's call her Kathy) was recently diagnosed with breast cancer, and I'm fortunate to be in her inner circle. We (her inner circle) know her well and she's been very direct with us when she was first diagnosed. We now know it's important for us as a group to have as much normalcy as possible and to let her do the talking if she wants to. Many, many times, she chooses not to talk about her cancer for multiple get-togethers in a row. That's just her. That's what she wants, and we show compassion for her by NOT talking about it until she opens the way to the conversation.
Kathy told us a story recently about an acquaintance of hers who was very, very insistent about getting her to talk to a complete stranger (a friend of the acquaintance) who also has breast cancer. "Can I give her your number?" the acquaintance asked. No, Kathy said, and she gently explained that she gets comfort from her friends who knew her prior to the diagnosis, and she would be very uncomfortable with starting off a relationship with someone just because they both had cancer. A couple weeks later, the acquaintance asked again, and Kathy again said no. The acquaintance ended up putting the phone number of her friend in her mailbox, then asked about a week later if Kathy had called the other woman. No.
While it may seem like Kathy was "rejecting compassion," I would argue that the acquaintance was lacking compassion by insisting on a type of coping mechanism which Kathy clearly did not want to use. It might be a good way of dealing with cancer for many people, but it just isn't the way Kathy is dealing with it. And that's ok! Unfortunately, the acquaintance just didn't get it.