So, it turns out that Toyota makes an All Wheel Drive version of the Sienna. The AWD version does not have a place for the spare tire due to the extra axles, so they sold this version with "Run-Flat" tires, which are supposed to be good for up to 100 miles when flat. Contrary to my expectations, these are not the foam-core tires, but just regular tires with thicker sidewalls, and they apparently barely work for the purpose intended. It doesn't seem as though they require special rims, and apparently regular radial tires will fit on the same rims as the run-flats. On the Penshare Sienna, they'd put plain Yokohamas on the back, but the front ones may still have been the run-flats; they were Bridgestone, and didn't say "RFT" on them as far as I could tell, but I didn't think to jot down the tire number so I could look it up.
Links:
http://www.siennachat.com/forum/89-2011-january-2010-3rd-generation-toyota-sienna/7897-new-tires-replacing-run-flats-nearly-new-2011-limited.html
http://townhall-talk.edmunds.com/direct/view/.f0e6c84
http://www.cargurus.com/Cars/Discussion-t29612_ds437434
http://news.consumerreports.org/cars/2011/06/more-run-flat-tire-wear-issues-on-2011-toyota-sienna-xle-awd.html
The run-flats for later Siennas are 18", earlier (like the 2007) are 17".
I looked up the tire in one of the photos of one of the Siennas posted online, it was Bridgestone B380 and found that yes these are run-flats.
