1 Mercutio: {pointing at Ophelia talking to Robert Pakington, MP} That guy is the actual Robert Pakington, MP.
1 Shakespeare: So?
2 Mercutio: He’s supposed to be murdered! Today! About ten minutes ago, in fact.
3 Shakespeare: You brought us to the exact place and time that the murder took place in real history??
4 Mercutio: Well... it’s not history any more...

Eh... it's probably all right. Someone got murdered in the right place at the right time.

In fact, someone pretending to be the correct historical murder victim.

Which suggests an interesting time travel story premise: Send actors back in time to pretend to be various famous murder/assassination victims, and save the actual victims. You could then bring them to the present and have them continue to contribute to society.

For example, instead of being killed by a Roman soldier, Archimedes might be rescued and live out another productive decade or two.

Or instead of being killed in a duel at the age of 20, after already having developed a whole field of mathematics, Évariste Galois might be rescued and.. wow, who knows what mathematical discoveries he could still make?

The hard part in all this is finding the actors to replace these people just before they're killed. I suppose you could recruit them from a 16th century London pub.