Open source inherently means you can compile the code locally,

Open Source means more than that. It is defined here:

https://opensource.org/osd/

If you use the phrase "open source" for things that don't meet those criteria, then without some clarifying context, you are misleading people.

for free.

Free Software is not the same as "software for free". It, too, has a specific meaning, defined here:

https://www.gnu.org/philosophy/free-sw.html

When the person to whom you replied wrote "free software", they were not using it in some casual sense to mean free-of-charge.