As someone who has negotiated with AWS at the $1m/month level this is completely false.
There's certain products of theirs that they just aren't going to negotiate on, because they know they've got you, whereas others the clouds part and discounts rain down.
It certainly used to be this way when AWS had less competition, these days there's an Azure/Oracle Cloud/Rackspace/Google/etc alternative to most of their greatest hits, which gives a greater negotiating edge.