I read it top to bottom. Samsung is not a partner in the LTE build out. They want Samsung LTE devices on their network. If Apple wins, they don't get those LTE handsets on their network and are loosing out on potential profits. That's why they wrote the position. And so did T-Mo. And as a fun little fact, the court accepted VZW and T-Mo's brief and denied Apple an opportunity to respond.
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Samsung is a network partner, along with Motorola, and Nokia-Siemens. They are helping Verizon to build their LTE network.
And, no offense, but you really think that Apple wants Samsung products banned? Of course they don't. They want Samsung to cough up money for infringing on design patents, and change the offending designs (most of which are software related). Samsung's already begun to do that, btw, as newer builds of GSII updates have infringing features removed. Apple's endgame is not blocking Samsung's sales, its the removal of those features and a royalty payment from Samsung.
Go read Foss patent's analysis again; he clearly said Verizon chose the weakest position in their statement. If Verizon really intended for their amicus brief to be anything other than a lip service, they wouldn't have focused on the weakest, and least defensible position for samsung, for their argument. T-mobile's a whole other can of worms; for whatever reason, Apple snubbed them in negotiations for an iPhone, a point that will certainly be hammered home by Apple's lawyers. Oh, and you missed this little nugget that will also certainly be brought up as a reason why Verizon's Amicus shouldn't even be considered:
FOSS Patents: Shocker for Android OEMs: Google document proposes giving Motorola time-to-market advantage to build Android "lead devices"
As for Apple's response; what she actually denied was a formal written response because Apple already gave it when the briefs were first given consideration. You bet your ass Apple will tear those briefs to shreds in court.
BUT, all that doesn't change the fact that Verizon and Apple's relationship hasn't changed. If it was as big of a deal as you are making it out to be, Apple would have voided the contract with Verizon and took its iPhones home. Apple doesn't mess around with stuff like this. And you can bet that Verizon's shareholders would be none too pleased that millions of potential iPhone customers went along with them.