Everyone deals with their grief differently. Personally, I believe I will be reduced to a pile of sobbing flesh for quite some time after I lose any of my animals. I'll probably need someone there to take me home. Will I be embarrassed about letting someone see me 'ugly cry'? Maybe once the grief clears out of my mind enough to let me realize that the world is still there.
If you feel you can handle being there for someone else during their time of sorrow, perhaps you could let your friend know that. Maybe she offered because she knows that she'll need someone there for her.
On another note, I'm sorry to hear about your cat
"He is your friend, your partner, your defender, your dog. You are his life, his love, his leader. He will be yours, faithful and true, to the last beat of his heart. You owe it to him to be worthy of such devotion."