Oh how irritating!
NO, a parent cannot insist, that a sibling is also invited.
That Mom, probably just wants both her kids out of the house and does not want to deal with the other child being at home "nagging" to go play too.
There is NOTHING wrong, with ONLY inviting your child's friend, over to your house. And you do not have to invite that kid's sibling.
You only invite, your child's, friend.
And it is up to that other parent, to deal with it. And to deal with her kid, that is home.
I have 2 kids, who always have friends over at our home. ALL of my kid's friends, have siblings. Some have more than one sibling. I DO NOT, invite ALL of that family's kids over. I only invite my child's friend.
And its fine. And it is fine with those other Moms. Because, the "play date" or social, is for that child and THEIR friend or friends.
However, IF my daughter or son, is also friends with those siblings, then I MIGHT, invite the siblings, too. But it is up to me. And I WILL say "The girls need their own time today without their siblings." Or "My son needs his own time, with his friends only." And I also tell that to my own kids. And its fine. EACH OF MY KIDS, have their own, friends. And they have a right to have their own time, with their own friends. Without their sibling. Each child has their own, friends and life and socials and invites.
This is life.