Interestingly, with OpenDNS, this does not show up using the any query:

$ dig @208.67.222.222 any eff.org

; <<>> DiG 9.9.2-P2 <<>> @208.67.222.222 any eff.org
; (1 server found)
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 61530
;; flags: qr rd ra; QUERY: 1, ANSWER: 5, AUTHORITY: 0, ADDITIONAL: 1

;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
;; QUESTION SECTION:
;eff.org. IN ANY

;; ANSWER SECTION:
eff.org. 3756 IN A 69.50.225.155
eff.org. 6413 IN NS ns6.eff.org.
eff.org. 6413 IN NS ns2.eff.org.
eff.org. 6413 IN NS ns1.eff.org.
eff.org. 507 IN SOA ns1.eff.org. hostmaster.eff.org. 2014031300 3600 1800 604800 1800

;; Query time: 380 msec
;; SERVER: 208.67.222.222#53(208.67.222.222)
;; WHEN: Fri Mar 14 22:26:33 2014
;; MSG SIZE rcvd: 153

Though, explicitly specifying the NAPTR type does display it:

$ dig @208.67.222.222 -t naptr eff.org

; <<>> DiG 9.9.2-P2 <<>> @208.67.222.222 -t naptr eff.org
; (1 server found)
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 65029
;; flags: qr rd ra; QUERY: 1, ANSWER: 23, AUTHORITY: 0, ADDITIONAL: 1

;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
;; QUESTION SECTION:
;eff.org. IN NAPTR

;; ANSWER SECTION:
eff.org. 6304 IN NAPTR 300 10 "" " !!!!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 310 10 "" " !!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 320 10 "" " !!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 100 10 "" " !!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 110 10 "" " !!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 120 10 "" " !!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 130 10 "" " !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 140 10 "" " !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 150 10 "" " !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 160 10 "" " @@@@@@@@@@@@@@@@@@!!!!!!!!! !!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 170 10 "" " @@@@@@@@@@@@@@@@@@!!!!!!!!! !!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 180 10 "" " @@@@@@@!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 190 10 "" " @@@@@@@!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 200 10 "" " @@@@@@@!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 210 10 "" " @@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 220 10 "" " @@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 230 10 "" " @@@@@@@!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 240 10 "" " @@@@@@@!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 250 10 "" " @@@@@@@!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 260 10 "" " @@@@@@@@@@@@@@@@@@!!!!!!!!! !!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 270 10 "" " @@@@@@@@@@@@@@@@@@!!!!!!!!! !!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 280 10 "" " !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " "" .
eff.org. 6304 IN NAPTR 290 10 "" " !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " "" .

;; Query time: 507 msec
;; SERVER: 208.67.222.222#53(208.67.222.222)
;; WHEN: Fri Mar 14 22:28:22 2014
;; MSG SIZE rcvd: 1876

With other resolvers such as Google public dns, or DNS Advantage, it does show up with the any type. Can anyone explain, why it doesn't show up with OpenDNS using the any type?