I do recall the criticism from her sycophants, even CNN and MSNBC, as you point out, that she owed it to her supporters to make a public appearance.
Have heard reports about her being a basket case that night/morning.
The only proof I have as to the validity of her making a call was the fact that Trump acknowledged her doing so in his victory speech. I would not be surprised if the call was not actually placed by Bill who covered for her.
They weren’t necessarily calling for her to concede. They were embarrassed that their candidate didn’t even have the decency to come out herself and address the people who had been sitting there in her election party headquarters all night.