Fortunately this just isn't true. There is a lot that can be done about a cat who stops using his litterbox - you just have to find the reason for the behavior change and make adjustments within your own home.
The first thing you should do when your cat has changes in their bathroom habits is to take your cat to the vet. Just because an animal isn't acting sick doesn't mean there isn't something medically wrong. There have been many cases of both cats and dogs who have urinary tract infections where the only symptoms is frequent accidents.
If your cat has been medically cleared then you need to consider a few other things. First of all -- cats can go for years with the same litterbox set-up and not have a problem. Then one day -- sometimes for a reason only the cat knows, they will start to not use their toilet area consistently.
Some other things to consider when trying to resolve this problem are:
Do you have enough litterboxes? Experts recommend that you have one box per cat plus an extra in different areas. Having two litterboxes side by side counts as only one box.
Is the box big enough? Many of the commercially sold litterboxes are too small for many cats. Try to get a bigger box, or purchase a large, flat storage box to use in it's place.
What kind of litter are you using? Typically cats do not like litter that is scented or has a deoderizing agent. It may smell better to us, but it could keep a cat away. Purchase several different types of litter and set them out in different boxes. The box your cat uses tells you which type of litter he prefers.
How much litter are you using? Most people have the motto that "more is better". But if there's too much litter the cat may feel that the surface under his feet are unstable and not feel comfortable in his box.
How often are you cleaning? Cats are extremely clean animals. It's recommended that a litterbox be scooped at least once a day. Cats don't want to use a dirty toilet any more than we do.
How noisy is the area where the litterbox is kept? Did something scary happen in the environment where the litterbox is kept while the cat was there? Keep litterboxes away from heavily trafficked areas, and away from appliances such as the furnace or washer/dryer. You may try moving the box to a new location.