Is this an illegal tie?

Amazon has told publishers that they have to use its in-house POD [Print On Demand] services. Publishers dont like it:

As you probably know, Amazon.com purchased POD publisher/printer Booksurge a few years ago. Since then, they have contacted us from time to time about listing some titles through Booksurge. We had used Booksurge a few times in the past and were not happy with the print quality of the books. So we always politely passed on the various offers and went about our way using Lightning Source (LSI) as our printer (and having the books distributed through Ingram, owner of LSI).

Despite ownership of Booksurge, Amazon continued to order print-on-demand titles through Ingram/LSI (LSI even drop-shipped the books for Amazon). So everything worked smoothly until last week, [when they told us that] only print-on-demand softcovers and color books that were printed by Booksurge would be available directly through Amazon in the future.

Is this tie illegal? Here is the answer from a colleague at ERSGroup.com:

In most circuits, a rule of reason finding against the defendant requires 4 elements:

1. Market power in the tying good. (Plaintiffs can meet this by showing that the defendant has more than a 30 percent share of the tying market.)

2. Purchase of the tying product is conditioned on purchase of the tied product.

3. The tying and tied products must constitute separate products (no left shoe/right shoe).

4. A not insubstantial volume of commerce. (Courts have used a very low threshold for this.)

In most circuits a 5th factor is required to make a per se case:

5. The tie has (or will likely) adversely affect competition in the tied product market.

Here the tying good would be on-line sales of books and the tied product would be BookSurge. If the plaintiff could show that Amazon has market power in the sale of on-line books, the plaintiff would have a pretty good chance. (This requires a market definition that excludes brick and mortar stores.) Also, if there is a dangerous probability that competion [is lessened] in the tied product market ("POD books"), the plaintiff could very well make a case that this is a per se violation.