I could be wrong, but I think the DoT damage is inaccurate because the combat log doesn't track it after the initial damage, not because the parsers choose not to read it (or read it incorrectly). Doesn't really matter who reads the data if the data just doesn't exist.
It was either that or the log not accounting for crits. I'm not sure, but I remember back when the parser discussions were still young that people were claiming DoT inconsistency as a combat log issue.
If I'm right (which, again, I may not be) then 3rd party programs would work just as well as an internal one if SE just updated how the log registers DoTs.