Fischer Insecure?

Here on Top eBay Chess Items by Price, Fischer autographs are frequently featured. The last one I can remember was Fischer's Doodle, although there might have been another since then.

If the only unusual aspect of the item pictured below was the signature itself, I wouldn't use it, but the item tells a story about Fischer. It was titled 'Chess Champion BOBBY FISCHER - Autograph Letter Signed' and sold for US $850.00, Buy-It-Now.

The description added,

8½" x 11" autograph letter signed on the bottom of a collector’s letter to him requesting a photograph, February 21, 1962.

The full request in the letter said,

As a great admirer of your superb talents in the field of chess, I would appreciate a momento in the form of a personal note signed, and if possible, an accompanying photograph.

Fischer replied,

Thanks for your kind letter. Since I wish you to remain an admirer I won't send you my picture.

Was the 18-year-old Fischer not as sure of his looks as he was of his chess?