Does wearing just one piece of a uniform equal being out of uniform?

Without knowing the full context of the situation, I'm going to make a reasonable assumption that due to the three people in this situation were military, that this occurred at an on-post gym.  That said....

14–4. Occasions for wear

The PFU and the IPFU are authorized for wear on and off duty, on and off the installation, when authorized by the commander. Soldiers may wear all or part of the PFU or IPFU with civilian attire off the installation, when authorized by the commander.

AR 670-1 no where authorizes anyone to mix IPFU uniforms ON the installation. 

Wear of military and civilian items.

(1) The wear of a combination of civilian and military clothing is prohibited, unless prescribed in this regulation or other authorization documents approved by HQDA.

So, even those post-level "blue books" have no authority to change the uniform guidelines unless they get HQDA approval.  

In accordance with chapter 45, section 771, title 10, United States Code (10 USC 771), no person except a member of the U.S. Army may wear the uniform, or a distinctive part of the uniform of the U.S. Army unless otherwise authorized by law. Additionally, no person except a member of the U.S. Army may wear a uniform, any part of which is similar to a distinctive part of the U.S. Army uniform.

So, all those army wives wearing their husbands' uniforms are wrong.