The isotope ratios of Deuterium vs. regular Hydrogen in comet water as compared to Earth's water is making the "Comets brought the water" theory looking less and less likely. Granted, we haven't visited a TON of comets, but the ones we have, like Rosetta is doing right now, are not making it look good.
That said, the evocative, but inconclusive "Martian fossil microbes" found in AH84001, and now some other meteoroids, who's isotope ratios indicate a very high probability they are indeed chunks of Mars, that some limited panspermia has happened at least in the local Solar System is a distinct possibility.
It would also make sense since Mars was smaller, it would have cooled faster than Earth, the Thea collision that formed the Moon withstanding or not, and would have had liquid surface water and a benign climate much sooner than Earth did.
No surprising, and not indicative of a negative. In the early solar system, elements and isotopes did fractionate w.r.t. Orbital radius, (one reason why inner planets are rocky, outer are less so), so it's not that weird that isotopic differences between hydrogen isotopes and thus water (especially given the relative mass differences) on inner planets (regardless of being deposited by cometary bodies during accretion or not) would be different than cometary bodies on higher semi major axis orbits (like what are seen today).
Also, it's a matter of time in how one phrases the argument, as cometary impacts during accretion is simply part of accretion, (and thus the basis of the non-extraterrestrial water theory) while others regard the extraterrestrial water to occur after the main body solidified. Two sides of the same coin.
Since any ice-ball is properly termed a comet, regardless of what side you agree with, any water on earth was likely frozen out, condensed, accreted into ice-balls, and then deposited in the growing or already formed planet...so "water from comets" is (while ambiguous in terms of time) pretty much accurate.
The other argument is that earth now, and even more so during formation is unable to gravitationally capture hydrogen on a long term basis (net loss is greater than net gain), so accreating hydrogen and then reacting it with a created oxygen to form water over time doesn't pass muster. In fact, due to charged particle impacts and UV disassociation of water, we actually continually lose hydrogen even now.
(And helium as well, which is why it's so important to recycle it/not vent it...once vented, it's gone).