Socialist Progressives

Believe it means that.

But Bernie has directly said he doesn't believe in collective ownership and instead references the Democratic Socialism in Scandinavian countries which also does not believe in social ownership.

The more common term for that is the Nordic Model:

"Although there are significant differences among the Nordic countries, they all share some common traits. These include support for a "universalist" welfare state aimed specifically at enhancing individual autonomy and promoting social mobility; a corporatist system involving a tripartite arrangement where representatives of labor and employers negotiate wages and labor market policy mediated by the government;[6] and a commitment to widespread private ownership, free markets and free trade."

That's what he espouses which does not have social ownership.

I am well aware however that private enterprise which is socially owned is not an anathema to capitalism.