Owned? No, it doesn't mean that.

Directly financed? I wouldn't call it a subsidy otherwise: https://www.google.com/search?q=subsidy&oq=subsidy

A subsidy can exist in effect when the terms are overly favorable and not at market rate.

PARC never had substantive DOD funding, it was funded by the largess of Xerox. Bell Labs did do government work, but was largely funded by the Bell Operating Companies, in the form of a royalty.

Exactly, the biggest research driver is military spending. Procurement is a huge way in which these companies were funded, eg the DOD bought 90% of computers in the 50's and 60's before they became viable as consumer devices in the late 70's.