Kukkiwon rank is only automatically recognized in Kukkiwon schools, and the same is true for every organization's credentials. Any recognition or acceptance outside of that is up to an individual's discretion. While no one can take away the hard work and dedication it took to earn the rank you hold, it is cavalier to think you should start at anything but a white belt when joining a new school of a different style or organization. If the new instructor or organization decides to accept you at the rank you hold, then great, but do not expect it. Now that we've established that, let's explore what I mean when I say international certifications matter.
When it comes to the arts we love, the majority of them are headquartered overseas. Therefore, it is only logical that they are the ones to issue credentials in their art unless they have specifically appointed individuals here to do so in their stead (this will be important in a moment). If the headmaster of an art cannot walk into your school and agree that you are in fact teaching their art, which includes being properly licensed to do so, then you're not.
For example, there are many schools and organizations claiming to teach Jidokwan. However, the Jidokwan as an organization is still alive and thriving. They are active in issuing rank and licenses to their members. Therefore, unless you're certified by them, can you really say you're Jidokwan?
NOTE: Some have wondered why the image of the certification is blurred in the image above, even going so far as to say it was done so maliciously in order to lie about what level was actually obtained. This is absurd, considering the official website of the International Meibukan Goju Ryu Karate Association clearly lists all active instructors with their rank. Rather, Meibukan bylaws strictly forbid the public display of certifications online as it is too easy to forge documents in the digital world we live in. You might be able to find a handful floating around in a Google search, however none have been issued by Meitatsu specifically as it is his rule as of this writing.
The three major organizations here are USA Judo, US Judo Association and US Judo Federation. All of these, collectively called the national governing bodies, fall under the authority of the International Judo Federation which exists to promote the sport of Judo. However, other organizations (such as the US Traditional Kodokan Judo Association and the Judo Black Belt Association) exist to promote the complete art of Judo as laid out by its founder, Kano Jigoro, not hindered by the current rules and limited set of competition techniques.
This is no different than the relationship between the Kukkiwon, World Taekwondo, and the Kwans themselves. World Taekwondo (formerly WTF) oversees international competition, and Kukkiwon rank is required to compete. In fact, this is the only true necessity for Kukkiwon rank. Since the inception of Korean Karate long before the name Taekwondo was even coined, the Kwans have been responsible for the training and certification of their students. Just because they have adopted the minimum standards laid out by the Kukkiwon for universal certification (for the purpose of allowing their students to compete internationally) does not mean their authority or prominence has been stripped from them. Chungdokwan, Jidokwan, Moodukkwan and the others all continue to exist independently and issue their own rank.
Another example of an organization here that has legitimate authority to exist despite breaking away from their Japanese counterparts is the Daito Ryu Ginjukai. Formed by Howard Popkin and Joe Brogna, they were given permission by their instructor (Okamoto Seigo, founder of Daito Ryu Roppokai) to branch off. This is not the same as someone choosing to continue teaching a Japanese martial art that is alive and well but choosing to do their own thing, continuing to issue rank and licensing in the art without permission. The Ginjukai was established with Okamoto's blessing, just like the Meibukan was established with Miyagi's blessing as I stated above. The ethnicity of the instructors is irrelevant, the protocols were followed to maintain the art's integrity and line of transmission.
Now, one counter argument I've heard is that we are Americans and so having a piece of paper from the other side of the world that most people can't even read has no importance. But they fail to realize it's not about where the piece of paper comes from. After all, an address is not a credential (although some Western instructors who happen to live overseas like to pretend it is). What matters is who is signing the piece of paper, and as I've said above, the authority to issue rank, titles and licenses comes from the headmaster or governing body of the style or organization. For the majority of the arts we are discussing, that person or organization currently operates out of Japan, Okinawa, Korea, etc. So therefore, that is where documents must come from.
Should that change, as in the system was passed down to someone in another country, then that's where documents would come from moving forward. This was the case for Tanemura-Ha Shindo Yoshin Ryu, currently overseen by Toby Threadgill in Colorado, along with several other koryu (pre-1868 Japanese systems) passed down to Western instructors. Despite being founded in feudal Japan, they are headquartered here. Receiving a document from Japan would be meaningless, because their headmasters are here.
Hopefully I've made my point, that the address on the envelope doesn't matter but the signature on the certificate does. If the legitimate authority to issue that certificate lives in Japan, you need to pay for postage. If not, such as in the case of the art being passed down to someone here in the States or even a new art created here in the first place (like American Yoshinkan Aiki Jujutsu, the art I have been blessed to inherit), then a certificate from elsewhere has no value. Like everything else, legitimacy comes down to what you claim.