That's a good point. Maye you could put a small warning on the page if they disable 'POST' that there might be leakage of their search terms to the sites they visit?
"Hello dear user, you probably know exactly what you're doing, but on the off-chance that you don't, please realize that disabling the POST option for https connections may leak your search terms to the visiting site".
The problem is not that the referer leaks to the sites you click through to. The referer leaks to sites as soon as the results page is displayed because there are externally hosted images embedded in the results page.
"Hello dear user, you probably know exactly what you're doing, but on the off-chance that you don't, please realize that disabling the POST option for https connections may leak your search terms to the visiting site".
Or something to that effect.