All parsers read the exact same combat log. The same log you upload to TORParse. That same log will have a TORPArse accounting that might not mesh with the MOX accounting, that wont match the SWMON accounting and wont match the ACT account despite all of them reading the exact same combat log. Which proves the point that if one varies from another then they all are not always accurate. You may claim TORParse is perfect but if it has to read the same combat log as every other parser out there then there is doubt. No parser is 100% accurate. Combat start/stop times effect things (parser A waits for 5 seconds out of combat to finish vrs parse B that waits 3 seconds, vrs parse C that waits 10 seconds etc). Also logs are just text files...easy to manipulate. All this is why so many games refuse to include a dmg meter in game because of how fickle they are and can be manipulated to report extraordinary high or shocking low damage. Data is only as good as the method used to collect it...and the combat log files are not good/precise. They were added as a concession to everyone wanting DPS meters and not supported (by an Official TM SWTOR DPS METER) because of the inherent differences of various reporting tools.
I can't argue against SWmon and ACT (never used them), but the primary difference between MOX's parser (the overlay) and TORParse is that MOX has to read the file as it's written, where as with TORParse there are no modifications being made to the log as it's read.
As for it waiting 3-5-10 seconds before it starts parsing, TORParse doesn't do that because it's not an active parse. It only registers from when the log says "Character Enterss Combat" to "X Kills character/ Character leaves Combat."