I think the issue is that BI has to decide on so many lines of text to send in the email - when you get the email of an error - it isn't your entire log since the beginning of time or the most recent month and it only sends out so many lines. When I look at mine, it will cut off mid line as it is like it only sends so many characters or lines of text.
Plus like I said, as long as I have been using BI, the log in BI isn't as inclusive as the full .txt log and it probably sends in email the BI log that if for some reason it didn't decide to capture the error in that log (but is in the full .txt log) then you won't see it in an email.
That doesn't make it right, but I suspect not enough people use this feature so it hasn't necessitated BI looking into further. Hopefully you sending a request can fix that!