The article mentions various RSA implementations that have had problems. The other thing is, since they do audits and are telling you to avoid RSA, the advice obviously isn't 'a properly audited RSA is fine'. "it's actually ok to use RSA" is not a reasonable conclusion to draw from this piece.
I think the crux of the argument is summed up here:
> Developers could theoretically build an ECC implementation with terrible parameters and fail to check for things like invalid curve points, but they tend to not do this.
So, it's just about trusting developers to implement a different algorithm properly.
