The observed number of accident X=3 does not lie more than two standard deviation from the mean, but it is close to the boundary. Thus the observed result is not highly improbable, but it may be sufficiently improbable to warrant an investigation.

This is a conclusion after crunching some numbers on the number of accidents in a month. Forget about the rest if you’re a layman to statistics, looking closer to the bold part, at one time, I thought I can get the drift of the message based on the calculations and the rule of statistics, but at another, I manage to come up with a totally different viewpoint. I started to wonder my mental faculty if it still serves me well.
Can you, who are good, show me the real meaning of those?

PS: How to see these kind of ‘negative negative’ or ‘positive negative’ unfold???

The first part of the sentence is saying that the observed result is (only) moderately unlikely (i.e. not extremely unlikely). We understand that the more unlikely a result is, the more it deserves (warrants) investigation. Something extremely unlikely would definitely deserve investigation, and something not at all unlikely would not be investigated. Our case, moderately unlikely, lies somewhere on that spectrum near the boundary of “investigate” and “not investigate”, probably just on the side of “investigate”. Thus it may be “sufficiently improbable” to warrant investigation.

First, the confusion is worse confounded.
Later on, it seems like what you said makes plenty of sense.
Will try to write again in case I had any more confusion.
Thanks so much.