> REQ-1: A NAT MUST have an "Endpoint-Independent Mapping" behavior
While Linux netfilter behavior is "Address and Port-Dependent Mapping".
As Linux netfilter implements both NAT and firewall behavior, it is relevant for the discussion which parts of overall netfilter behavior falls into 'NAT part' and which into 'firewall part'. There is clear distinction - DNAT/SNAT rules in nat table represent NAT behavior, while REJECT/DROP rules in filter table represent firewall behavior.
As Linux-based SOHO routers are usually configured with both NAT and firewall netfilter rules to implement both NAT and firewall behavior, one cannot answer question 'Does NAT filter traffic?' based on external behavior of such SOHO routers, but has to analyze which part of the network stack is responsible for such behavior, or how the same network stack configured with just NAT rules and no firewall rules would behave. And here the answer is no, it would pass traffic (that do not match existing connections) unmodified.