opendkim-testkey: key not secure

I set up Opendkim milter to work with postfix on my machine. Now email is signed & verified correctly i.e. email source code shows DKIM-Signature header.

TXT record on the authorative dns is set up like this:

┌───┐
│ # │ root > server > ~
└─┬─┘
  └─> delv -t txt dkim-domain._domainkey.domain.eu
...
...
dkim-domain._domainkey.domain.eu. 1780 IN TXT   "v=DKIM1; k=rsa; p=MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEA8drA4hH8gJaVpLaHhtQonhpOeanMo/oPmrAVehP3lBYAjsoxifCIclLqJo7kk0maelqu9SIN9ttQ0boCzEiQBMO1" "c1P+Sj/PxphZB71c8VNhqMJ32VG6Ky3ZD4Tds39Vye/wsWdi+842MUT3Z2dJnxS2AAG4pSkjaytFPCs0J94OUQC0tDErbnsMZh+gg+7IsYgND8FR/cRDzpXjD0qFJk4Cnc1q27WorPAGAiRsRfLt9u" "gkYgQRwapnofmKJ3hk/L8096YR7gan60L4+RGojsx5ppTdIEhYasyK9MokefmVeNyGwVXTJchqG8vhcg9uGjGy9mPiPg4B2TQgEBPwyQIDAQAB"
...
...

So on first glance everything is okay but when I run the diagnostics on my machine it says this:

┌───┐
│ # │ root > server > ~
└─┬─┘
  └─> opendkim-testkey -d domain.eu -s dkim-domain -vvv

opendkim-testkey: using default configfile /etc/opendkim.conf
opendkim-testkey: checking key 'dkim-pistam._domainkey.pistam.eu'
opendkim-testkey: key not secure
opendkim-testkey: key OK

Note the key not secure answer. I read from this answer that warning exists because DNSSEC is not enabled. But DNSSEC for my domain domain.eu is enabled. according to the DNSViz.

ADD:

It may be that the topic I linked to earlier is missleading, because I later read an answer here, suggesting that warning is due to too permissive privileges regarding the key pair! I set user rights on the key pair and their folder like this:

┌───┐
│ # │ root > server > ~
└─┬─┘
  └─> ls -l /etc/opendkim/keys/
total 8
-rw------- 1 opendkim opendkim 1675 Dec 30 08:45 dkim-rsa-private.key
-rw------- 1 opendkim opendkim  451 Dec 30 08:46 dkim-rsa-public.key

┌───┐
│ # │ root > server > ~
└─┬─┘
  └─> ls -ld /etc/opendkim/keys/
drwx------ 2 opendkim opendkim 4096 Jan  1 07:18 /etc/opendkim/keys/

So it should be secure... But it is not.