Can Veneers Hide Thininng Enamel?

If the front of your tooth is thin and there is enough enamel then you can get veneers. 

If the back of your tooth is damaged and thin then I would recommend a crown to cover your entire tooth.

If the thinning is the result of loss of enamel on the inside, then veneers will not solve the problem. You are better off with a full coverage option of crowns.

You mentioned your two front teeth are extremely thin. Your dentist does not recommend veneers because the problem is in the back of the tooth.  Veneers are a wonderful choice to give you two very beautiful front teeth.  They wrap around the tooth but do not totally cover the back.  No one can see the back, so this should not be the cause of your embarrassment. Veneers would be less bulky than crowns or caps and your smile would be more natural looking and cosmetically pleasing.

Veneers are designed to replace the enamel on teeth that is missing or damaged. Even though the veneer does not cover the enamel very much on the back of the tooth, it will to some extent. I believe them to be a better option than crowns or caps that can make the teeth look big and bulky if done improperly. If you do nothing and end up fracturing your teeth off, then root canal treatment and crowns will be your only choice. Do veneers first to strengthen the teeth back and then get a night guard to protect the remaining enamel.
Dr Thomas

Veneers don't only attach to the front of the teeth. More often than not veneers wrap around the tip of the tooth as well as the sides. With the introduction of dentin bonding technology a veneer can attach to a tooth with little or no no enamel and function very nicely.
If the problem is loss of enamel near the gum line on the inside, Lava crowns are the answer for you. I must agree with Susan that if the cause of your loss of enamel is acid reflux or untreated Bulimia you must get these problems under control or you will destroy any cosmetic work that is placed in your mouth.

In cases like yours, the first thing I do is find out what is causing your enamel to thin. Acid reflux? Grinding? History of bulimia? Restricted chewing envelope (a bite problem causing your lower teeth to grind across your upper teeth with too much force)?
After we find out the cause, we can treat it. And we can give you a gorgeous smile with veneers at the same time! If we need to reduce the acid environment in your mouth, we have treatments and products to do it. If I need to reduce the chewing forces on your teeth, I can do that. If you need night-time protection from grinding, we can provide it. I combine these treatments to give you a result that looks good, feels good, and lasts a long time.

Many dentists that discourage veneers don't know how to do them and don't understand their application. Depending on how much tooth structure remains, the bite forces and the condition of the remaining tooth structure (some teeth don't bond very well) veneers may work very well.
If not, full coverage crowns may be indicated.
Whichever is chosen, be sure all porcelain materials are used, not restorations with metal underneath.