Yojimbo and Sash of the War Champion. Shouldn't these work together?

[Syrul]

Sash of the War Champion wrote:

The wearer treats his fighter level as 4 higher than normal for the purpose of the armor training and bravery class features.

The Yojimbo Armor Expertise class feature wrote:

At 3rd level, a yojimbo selects one type of armor, such as chain shirt or scale mail. The yojimbo gains armor training, treating his samurai level as his fighter level, when wearing the selected armor

Wouldn't this imply that the sash improves the Samurai's Armor Training for their chosen armor? I believe it would, but I'd love more information to back this up.

Is there a similar archetype/item interaction that sets precedent?

[Cavall]

Sure