Yes, but the inclusion of a non-EU country in an EU programme as a special exception (not unique to Schengen) doesn’t thereby make it a non-EU programme, which is a natural interpretation of what you said
I never wrote that Schengen "is not an EU programme", I pointed out succintly that the countries in Schengen and the countries in EU are not the same thing.
In fact there are also EU countries NOT in Schengen. And there are countries in Europe but not in the EU which are not in Schengen either.
In fact there are also EU countries NOT in Schengen. And there are countries in Europe but not in the EU which are not in Schengen either.