So is this a copyright agreement or a EULA? Copyright agreements only cover distribution and if you something internally, it doesn’t cover your usage. Only if you distribute the code does it come into play.
Copyright covers four rights, one of them being distribution. It also covers creating derivative works, copying, and public performance. Many licenses based on copyright put restrictions on use; indeed, the BSL (the same license the author is thinking of moving to) does exactly this.
In the case of the GPL, you only need to provide source code to those you distribute the software to; that may be what you're thinking of with respect to distribution, but that's more an artifact of the GPL (and its goals) than copyright.
Copyright covers four rights, one of them being distribution. It also covers creating derivative works, copying, and public performance. Many licenses based on copyright put restrictions on use; indeed, the BSL (the same license the author is thinking of moving to) does exactly this.
In the case of the GPL, you only need to provide source code to those you distribute the software to; that may be what you're thinking of with respect to distribution, but that's more an artifact of the GPL (and its goals) than copyright.