I can't answer for EASA, though I expect it's similar to what we do here in Canada. The test aircraft of course needs a flight permit, as it does not meet the requirements for a full flight authority (usually a certificate of airworthiness). I'm not familiar with the EASA "Basic Regulation", so cannot comment that, but I expect it's more a matter of the fact that the aircraft, and some elements of it's operation cannot meet other regulations, rather than need not. It has been the case where I have test flown a completely conforming aircraft (which would be eligible for a C of A, other than I am deliberately exceeding a limitation (the reason for the test), so I could not meet the requirement to stay within that limitation, hence the need for a test plan and flight permit.
Generally, flight testing will impose more, and more restrictive regulations, so the notion that a regulation might not apply should be approached with caution....