No, that is not why the Earth is said to be 4.5 billion years old. It is said to be that old based on radiometric dating of earth, meteor, and lunar samples. Fossils are originally dated from the age of the minerals in which they are embedded. If similar fossils are found in other areas, then this is used as a quick way to date minerals in those areas.
If you think that's how scientists arrived at an age for the Earth, then I'd humbly suggest that your academic sources are probably mainly religious rather than scientific. It sounds like the kind of thing a pastor would tell to churchgoers to make them think scientists are dumb, rather than something scientists have ever said.
If you think that's how scientists arrived at an age for the Earth, then I'd humbly suggest that your academic sources are probably mainly religious rather than scientific. It sounds like the kind of thing a pastor would tell to churchgoers to make them think scientists are dumb, rather than something scientists have ever said.