Only certain weapons can deliver the final 1%/5%/15% damage to certain types of ship. The percentage and weapons are determined by flags in the table entry.
Sure, it'll say you got the kill, but kills are determined by how much non-beam damage was done to a ship. You get a kill if you did 20% or more of that damage, and also had the most damage against it of all ships that got 20% or more (whereas an assist is 15% or more damage when you did not get the kill yourself).
Example: In "Surrender Belisarius", you can easily get the kill for the Belisarius by hitting the ship with ONE Subach shot. The beam damage from the Psamtik's guns doesn't count towards kills. If the Psamtik weren't there, you could keep firing forever and never bring the Belisarius below 15% (I think that's the number, I'm assuming it has the same size flags as a Moloch).
If anyone has the exact stats/flag names, please post them here. I'm too lazy and tired to fetch them and copy+paste them from the Wiki.