I was baffled how this could happen. Stainless steel will pick up some scratches and stains, but it should be protected from rusting by a layer of chromium oxide (one of the characteristics of stainless steel and why we use it so much in the kitchen).
I was just starting to despair when I realized the reason for the rusting and found its solution.
My best guess is that the heavy-duty cleanser I'd used to scour my kitchen before leaving on my trip was the likely cause of the rusting. Bleach can strip away the protective chromium oxide layer and leave the steel below exposed to the elements, especially if left to dry on its own as I did. Additionally, stainless steel with less chromium content (which is to say, cheaper stainless steel) is more vulnerable to rusting.
The solution is actually fairly simple. Scrub the stainless steel surface to remove all rust and dry it thoroughly. The layer of chromium oxide will reform on its own over the next few days.
Many sources (see below) recommend using Bar Keepers Friend to clean away the rust. This is what I used and it definitely did the trick. If you'd like to go a more natural route, try using a paste of lemon juice and cream of tarter. In either case, use a plastic scrubbie pad for cleaning; using steel wool can cause further damage.
My table is now back to its usual shiny self, and hopefully, now it will stay that way.
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(Image: Emma Christensen)