There is no specific reason to believe ECC methods on these standard curves (or other well selected parameters) to be insecure. But at the same time if someone

There is no specific reason to believe ECC methods on these standard curves (or other well selected parameters) to be insecure. But at the same time if someone argues that the NSA could have influenced the parameters to create hidden weaknesses predicated on math unknown to the public, that argument can't be denied. It might even be supported on the basis that they could have easily closed off that argument but did not. (OTOH, equally I could argue that the same selection may have been used to make it stronger). As far as RSA goes, their usage involves fewer free parameters... but to get RSA up to the security levels people are demanding today require increasingly large and slow keys. If the crypto is too burdensome it'll get avoided, and thats worse than whatever speculation you might have about NSA weakening of EC systems.