The rule applies because Lin has an early qualifying veteran free agents exception. The early bird rule stipulates the maximum that can be offered is 175% of the salary (if above MLE) and MLE (league average salary) otherwise. If Lin had full bird rights Morey could have structured a 8/8/8 deal. Houston pays Lin 5/5/15 but that isn't important, because it's just money out of Houston's operating revenue. The amount that applies to the cap, and thus limits what moves Houston can make is 8/8/8 this is because of another rule where Lin's salary is averaged out in terms of the cap when he signs an offer sheet as a restricted free agent but does not apply to the matching team. So the Knicks pay 5/5/15 to their cap and to Lin. Houston pays 8/8/8 to the cap and 5/5/15 to Lin
The intent is to help you keep your own RFA. The intent was to close a loop-hole that Washington used to steal Arenas from Golden St. Golden State was powerless to outbid Washington. A team with a good RFA would NEVER be able to match anyone who could pay more than the Early-Bird exception. The important word in the previous sentence is NEVER be able to match. Asik would already be a Rocket without the rule. But now, the Bulls can exceed the Early-Bird and match.