But I suppose RTD needed to show that the Doctor had reached the limits of his hubris and, just as in the old Greek myths, he had to be brought low for it.
But the timeline for the grand-daughter of Adelaide Brooke could have still been preserved without Commander Brooke actually dying. Of course, the other two Martian colonists would not have been allowed to alter their fates and remain on Earth either.
What the Doctor should have done was to take the three survivors to another planet, where they would have no contact with their homeworld. That way, the authorities back on Earth would have had to assume that they had perished on the Red Planet as well, along with the others from their team.
The Doctor made this kind of offer at least twice before - to the Empress of the Racnoss and to Miss Hartigan as the Cyber-King. And that was for his enemies. He should have thought of the same option for these unfortunates.
As you might have expected from the good folks at Toobworld Central, we have two planets in mind where the Doctor could have taken them. And keeping with the no borders policy of pure televisiology, neither one is originally from 'Doctor Who', but instead from the classic 'Star Trek'.
The only requirements needed in choosing the planets would be that they were already inhabited by a humanoid species compatible to humans (iin case they needed to live undetected among the natives), and that there was no contact with Earth - at least in the "present day". (The timeline for "Waters Of Mars" had it taking place in the 2050's.)
So here are my two suggestions:
from the episode "Plato's Stepchildren"
The Doctor would have to drop them off after the edict against travel to that planet by other members of the Federation was put in place. That way there was an embargo to keep outsiders from learning about the three colonists. And before the Doctor left them in the "care" of Parmen and the other Platonians, he would have made sure that their bodies were doped up on triple doses of kironide so that they could be on equal footing against the other Platonians.
Granted, it wouldn't have been an ideal situation, but at least nobody else would have learned about them.
With the help of Mr. Atoz and the atavachron in the great library, the Doctor could have found new homes for the three of them in any of the past eras of the planet. As a Time Lord, the Doctor surely must have been aware not only of the Sarpeidonistas' ability to go back in Time, but also that they could live back then without affecting the timeline. This would have made Sarpeidon the better option as a new home for the three Martian survivors, in my not so humble opinion.