You can commit evil acts and still be Neutral. Some people might argue that the difference between True Neutral and Neutral Evil is that a TN assassin works for the money, it's just a job, and they don't really consider the "right or wrong" aspect of it, just as long as they get paid; whereas a NE might enjoy killing, go out of their way to make a victim suffer, and prefer killing innocents.
And if you counter by saying "But killing is wrong!" keep in mind that just about every Good-aligned character we've ever seen has killed people. Paladins kill sentient goblins because their boss tells them to. Miko tried to kill Roy and the rest of the OotS just because Shojo sent her after them. Hinjo tried to kill Redcloak at the docks, even though some people might argue that as an enforcer of law he should be trying to capture the enemy leader to put on trial for war crimes. It's all subjective.
And to further the points I made above, what's the difference between an assassin killing innocent people just because she was being paid, and a paladin killing innocent orcs just because he was being paid (a case brought up in On the Origin of PCs, where a paladin wanted to murder orcs who weren't hurting anyone and said explicitly he didn't even need to worry about alignment penalties for it).
Draz makes a very good point here. There is no way to say "anyone who does X must be alignment Y." People of ANY alignment kill other sentient creatures when it suits their purposes. There are, of course, some EXTREME cases where it's blatantly wrong to kill (i.e. striking down your defenseless liege). Barring such extreme cases, however, there is a TON of grey area in between, grey area where paladins and other good-aligned people murder sentient creatures all the time.
Here's an example:
the Ogres. They were raiding, robbing, and kidnapping... but as far as Miko and the Order knew, the Ogres hadn't actually
killed anyone. Yet instead of arresting them and bringing them in for trial, Miko proceeded to blatantly murder the entire tribe "just because they're evil." Is this really that different from what Therkla does?