The problem would be blurring or denoising meaningful information, but I don't know enough to say they don't do any denoising. I can imagine the data being noisy, but perhaps it isn't? shrug :D
Yes, accelerating MRI acquisition increases noise in the images as well as introducing aliasing artifacts. I think the issue is that some modern reconstruction methods (e.g. compressed sensing that was mentioned in the article) produce predictable biases, e.g. adding a risk of smoothing out details, but for ML we don't always know in what way it will bias the reconstructed image (add details, remove important information...), and I think that is what people often worry about.