I've seen a lot of takes on the GPL but this is a new one to me. As another comment points out, you only have to make changes available to others if you make the software itself available to others; either by distributing a binary or by using it to provide a web service.
But this is, fundamentally, the point of "Free" software: someone who uses a piece of software should be entitled to change that software as they desire. This obviously implies that if you make your own modified software available to others, they too must be able to make their own changes.