No one needs to be outside with the mourner. I haven't seen anyone stay with the mourner anywhere that I have been. There's also nothing in the picture stating this is needed.
In a sense, Kabbalat Shabbat is a "mix". Technically, men do not accept Shabbat until they say the song for the Shabbat day. This explains in part why the mourner is asked to wait outside - because he is still allowed to mourn.
For the others in the congregation, Kabbalat Shabbat is a joyous prayer that greets the Shabbat queen, and is a "preparation" for Shabbat acceptance. Thus, in a way, if a congregant sat with the mourner, in a slight sense, he is mourning on Shabbat, which is a contradiction for him.