You all are responding to this question with thoughtful insights and good mother-baby centered discussion.
When I read the question, however, I wondered if the RN who said that she'd heard that attempted breastfeedings count was coming from a different place. 

Where I work ABFs *do* count---but in a different way. 
They count as showing that the RN has done her job of being sure the baby goes to the breast at least every three hours. Whether the baby was showing readiness signs at that  moment or not doesn't matter. At least the mom and the RN tried.

We IBCLCs get wonderful fellowship teaching time to talk all about the importance of s2s to the newly-hired RNs. Some of them take it to heart (more and more do, it's getting better!). But once the newly-hired RNs are on the floor, some just follow the practices of the old RNs who insist on keeping babies swaddled. It takes a loooong time to change institutional practice.

Debbi Heffern, RD, IBCLC 

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