It could very well have resulted in an infringement suit against the producers of Married...With Children had they chosen the We're Not the Cosby's title. While titles cannot be copyrighted, identical or similar titles can suggest a similarity in the work produced itself and, in some cases, titles can function as a trademark.
This is often the case with television series, whose title will not only distinguish it from other series on television but will also become an important factor should related products and services connected to the series be marketed. Cosby's Fat Albert, for instance, is a trademarked title and is used for the marketing of a Fat Albert clothing line and related merchandise.
Trademarks do not need to be registered with the USPTO to be protected, although they gain more protection upon registration. Usually a producer, or an attorney, will do a trademark and copyright search before investing in a titled television show. Title and trademark clearance is now often required to avoid potential infringement suits. The costs involved in changing a title after production is expensive, and problems with a title can affect distribution rights and can result in a major loss of dollars for the producer.