How can I officially prove that a Bitcoin private key is owned by an entity?
A middle man trying to create a business around being a middle man with a technology thats supposed to remove intermediaries?

It seems like you could accomplish what you want with multisig wallet and counterparty.

In the example I have in mind, 

The issuer could create an asset that represents qualifications. The issuer could invite their practitioners to a 2-of-2 multisig address and send the asset to that address. 

Although we can't confirm if only those two parties have the keys, we can see where the asset came from (but it one scenario it can also be issued by the multisig address and never moved). We can rest assured that it would require both parties, one of which being the individual, to create a proposal to move the qualification asset. And these proposals will be rejected.

Another perk is that the asset can correspond to a centralized system.

Predictable, there's no place for your business in this mix, but that's probably the point, so I would like to thank you and your investors, in advance, for their charity in bringing this idea to the world. Should probably do an ICO