Saying “we are going to look into it” would obligate the White House in a way they don’t want and keep the issue alive for much longer, because they will continue to be questioned on it until they eventually still have to say “there’s too much weight being put into that.” Then they get criticized not only for “concluding” this, but for dragging it out.
By saying this when she did, she takes the hit now and it heals faster once the media starts chasing the latest laser pointer light.