I am not sure if things have changed in the 9+ years since this question last saw activity, but the current reading of the DELETE method indicates times have changed, based on the accepted answer:

The DELETE method requests that the origin server remove the association between the target resource and its current functionality. In effect, this method is similar to the "rm" command in UNIX: it expresses a deletion operation on the URI mapping of the origin server rather than an expectation that the previously associated information be deleted. (emphasis mine).

HTTP request methods are semantic intentions. The intent of DELETE is to remove the association between the URI and the target resource (not "actually get rid of the object" per the accepted answer).

If I receive a DELETE request, regardless of how I remove that association (actually deleting the record or marking it 'inactive/deleted/whatever'), the GET response (which ultimately satisfies the intention) should not return the resource from the requested URI. Does it matter if it physically exists or not?

Based on the current spec, anything that removes the association between the target resource and its associated URI mapping is the intent of the DELETE method.