It couldn't possibly be that the synoptic Gospels are just that because they all witnessed the events as stated, but just have slightly different takes on things. The same way that a dozen eyewitnesses to an event today will differing accounts despite viewing the same event.
Here are some things you have to think about:
1. We are not talking about just narration of the same events, we are talking about narration of the same events using the exact same words
2. Luke was not a witness of Christ. In fact, he SAYS he uses sources (Luke 1:1-3):
Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who from the first were eye-witnesses and servants of the word. Therefore, since I myself have carefully investigated everything from the beginning, it seemed good also to me to write an orderly account for you, most excellent Theophilus
2a: there were several histories at the time Luke wrote
2b: "handed down by the eye witnesses" means there were sources, both oral and written probably. It also means Luke was not one of them.
2c: it was drawn up under the patronage of a guy named Theophilus
In the conventions of the time, when you write history, you use other written sources. We have zillions of examples of this in Graeco-Roman historiography. I suggest a read of David Aune's
The New Testament in its Literary Environment for more information on Luke-Acts and ancient historiographical methodology. For example, Tacitus, when "quoting" Claudius' speech (for which we also have an engraved record) follows that engraved record, but then also feels free to make up parts, and to make Claudius sound better.
3. The only gospel which claims to be dependent upon eyewitness claims is John's.
4. None of the gospels has a named author attached to it.