I believe it's theirs. If I loan you my laptop brimming with free software, and you use it for a day, have I redistributed the software to you? No. You had us

I believe it's theirs. If I loan you my laptop brimming with free software, and you use it for a day, have I redistributed the software to you? No. You had use of a computer you didn't own executing the software, no copy was made. It's no different from the well-known SaaS loophole the AGPL attempts to close.