While the batteries themselves cannot go through the washing machine (or at least, it is strongly recommended against) the vests themselves can go through without being damaged. The vests that are machine washable simply allow the user to remove the battery before tossing it in with the rest of the laundry.
A few tips: be sure to use cold water, especially with the more delicate fabrics and pieces of outdoor gear. Also know that putting your vest or jacket through the washer might remove some or all of its waterproofing layer, reducing the overall weatherproof rating of the garment.