Like weddings, funerals just seem to bring out the special snowflake in some people. I think her demand was very rude. It doesn't sound like she was even that close to the deceased or the family. I agree with LeveeWoman, this is a situation where it is rude to ask. She tried to make it all about her.
At my grandmothers funeral, we had a private viewing beforehand in a side room for immediate family only. There was a family prayer and to say a few private words, and my grandfather placed some mementos inside the casket with my grandmother. Then we closed the casket and escorted her as a family into the chapel for the general funeral. That was our goodbye.
At the funeral, guests did come up to the casket to place a flower on top or just spend a moment beside, but one lady actually tried to open it. Thankfully the casket lid was locked down. It was so shocking and disrespectful to us and the impression it gave was that her
grief and wishes were so much more important than ours. As far as I know, she just went to the same church as my grandparents but wasn't a close friend or anything. I know it's not true, but if she had succeeded, it would have felt like she "undid" our goodbye.
I know it's a bit morbid, but there is/was (it hasn't been updated for a while it seems) an advice column called Ask Judy and another called thecheckoutline.org both by Judy Bachrach. It's like Dear Abby but all about end-of-life issues, the dying, deaths, funerals and what comes after http://www.obit-mag.com/viewmedia.php/prmMediaTypeID/297
edited to fix the web address