Yep, that would do it. I've made many Brewer's Best kits when I started out and they were fine. I bet the detergent (if any) and the drying agent left a residue that kills the head. The good news is that you can rinse those bottles as you use them (get all the yeast out and all the sediment with hot water) and then they'll be clean, and you can just use a no-rinse sanitizer like Star-san or Iodophor next time.
I know that the dishwasher seems easy, but sanitizing takes less than 10 minutes by hand. I start with clean bottles, and squirt sanitizer in them with a vinator, and stick them on the bottle tree. No kidding- 10 minutes or less!
If you still want to try something different, some people use the oven to sanitize. Neither the no-rinse sanitizer method or the oven method would leave any residue on the bottles.