There is no "true neutral position" in reality. Neutral is simply whatever is the currently trimmed position. The reason the game's neutral/default trim results in a nose-up movement, is because they had to set
something as the default trim setting at the start of a mission, so they decided to make it trimmed to stand still on the ground to avoid players accidentally rolling on the tarmac during start-up. However, the "ground trim" setting is somewhat aft of most flight and take-off cyclic positions. Therefore, when you cancel trim in flight, the nose pitches up as the cyclic is set back to the "ground trim" setting.
It's perfectly normal and realistic to trim the aircraft for take-off, as well as continually trim in flight.
In this video, you can hear a "click-click" just before the pilot takes off. That's him setting his trim for take-off from wherever it was set before:
http://www.youtube.com/watch?v=iG1E1lgTsLwOut of interest, you may want to watch the rest of the video and see how often he trims. Oh and yes, we know the HUD symbology is a little different in that version.
This is also explained in the User FAQ:
http://forums.eagle.ru/showpost.php?p=583711&postcount=42