Now you're on to something!
A real property owner agrees to display an advertiser's (sponsor's) graphics on a billboard for a certain amount of time. If, subsequently the billboard owner allows it to fall apart or become vandalized, or if they keep it up longer than agreed to and have someone re-paint it over and over again and the advertiser has a problem with it, that's really a contract issue - a question of whether the IP is being used as agreed. Similarly, in the case of the team kit, the sponsors agreed to have Biemme produce garments with their graphics on them. Now, if Biemme subsequently licensed the design of the kit or assigned its production to another maker, that would be a contractual matter. As it happens, Biemme explicitly denied that they permitted the (re)production of the kit, so presumably they held up their end of their bargain with the sponsors. That's what matters, and that's proof the HK kit is pirated.

We can be sure that A&S, Mokambo and the others agreed to the manner of placement of their logos on the design of the kit, but whether there were any stipulations regarding material and construction specs, extent of distribution or the assignability of production, etc., and what they may have been, we don't know. However, the fact that the kit was ever for sale by Biemme to anyone besides the team itself indicates a certain lack of exclusivity and opens up the possibility that cheaper versions were not illegitimate.