Claim number 1: Hair formula vitamins. These claim a variety of benefits. Grow hair longer, stronger, thicker, etc.
The truth is, the body can only use so much, and extra vitamins and minerals are either excreted in urine, or extras stored in fat. For a normal, healthy person, eating a balanced diet will provide enough nutrition and excess vitamins are unnecessary, and too much of some can actually be dangerous. My hero Sheldon Cooper from The Big Bang Theory put it best when he observed Penny shopping for vitamins, "While there is some benefit to taking a multi-vitamin, the body can only absorb so much. What you are buying there are the ingredients for very expensive urine."
The exception to this is if you are not healthy and/or do not eat a balanced diet. Some conditions do benefit from vitamins. I myself have Crohn's Disease and Lupus. A few years ago, my hair started falling out at an alarming rate. While it's normal to lose around 100 strands a day, I was losing so much that it would clog drains, have clumps all over the floors and furniture, gobs of it in my combs! After 3 bowel resections, I no longer absorbed B-12. And I was put on a folate blocking drug. Along with being iron anemic, and put on a restrictive diet. So I was put on B-12 shots, potassium (I forgot to mention I also had trouble keeping my potassium up), iron, a multi-vitamin, and finally folate. After being put on the folate, I started noticing quite a bit of regrowth in my crown area. After a few months, those bitty hairs were turning into short little clumps. Now my hair is almost back to it's normal thickness. So I am proof that health problems or poor diet (in my case, both, as the diets I am forced to eat to control Crohn's symptoms are very limiting) can benefit from added supplements.
Most often, though, hair product companies rely on silicones to temporarily "glue" splits and damaged cuticles down. The problem with this is that the glue is removed each time you sulfate wash your hair. And to remove most silicones, you do need a sulfate shampoo. There are exceptions, PEG and PPG modified silicones are water soluble, and there are a list of others that may be water soluble, or removed with a low sulfate shampoo. At any rate, each time you need to remove the silicones you are damaging it even more with sulfates. These silicones coat the hair, so they must be removed regularly. They can build up and suffocate hair. Not allowing moisture in, and ultimately causing more problems.
Keep in mind that it is normal to lose around 100 strands a day. In straight hair, these stands slip out throughout the day and aren't as noticeable. With wavy or curly hair, the texture does not allow for these hairs to slip out unnoticed. They stay stuck in their clumps, nestled up with their curly buddies, until we wash and detangle and physically pull them out with our fingers or wide tooth combs. So a clump of 100 hairs seems like a lot, all at once, but it is perfectly normal. Broken hairs are usually pretty obvious, since they are shorter. In conclusion of this claim, cleansing your scalp properly with a good massage, keeping up with your protein/moisture balance, and for very damaged hair, a hair cut, trim, or "search and destroy" for damage will go a long way for the health of your hair and scalp and reduce breakage.