I did the test. Apparently my glasses are clean. I quickly ran some water into a glass, hung the glass upside down for about 15 seconds, then dashed salt in from a shaker.
These are only washed in my dishwasher. As I stated before, I use Cascade Commercial detergent and rinse agent, and I have a whole-house water softener. I get great lacing on glasses.
For me, the story of rinse agents affecting head is bunk. Same with using a dishwasher. I suppose if you have hard water, you'll get some scale or other residue left on your glasses and that might have some effect.