Not true. A brita filter removes almost all the chlorine, copper, and heavy metals from water. Filtration does not need to be slow to be effective. It does not remove fluoride, sodium, etc. from water though, so it's definitely not perfect.
Make sure to change the filter every few months -- chlorine is added to water for a reason (prevent bacteria growth), so filtered water (of any kind) can be a breeding ground for bacteria (given trace nutrients).