In this scenario, the rights you’re leaving out are the rights to reproduce, distribute, and create derivative works. They’re exclusive.
You’ll find reputable t-shirt printers will refuse to print designs they know to be copyrighted.
No one would be claiming the printer or you came up with some copyrighted design, it’s the copying that’s an infringement (“copy”-right!).
Now, these printers also typically have you assert that you hold the copyright to the work, but my understanding is that just limits their total financial exposure by contracting with you; them producing the work would still be infringing.
Here, you aren’t even giving the bot a work to reproduce. It holds the work in its storage and will reproduce it for you when asked. That’s pretty cut and dry copyright infringement by whoever controls the bot.