Longest path is frequently different to true critical activities because it cannot handle multiple date constraints nor resource leveling.

If you are interested on identifying activities that are not critical at any specific moment but with high probability of becoming critical you shall look at statistical modeling.

Traditional definition of critical activities is, activities with no available float, that if delayed would delay the job finish date or any contractual milestone.

I believe it is mathematically correct but unfortunately some people that cannot accept critical paths can be multiple under multiple contractual delivery milestones or that these paths can be just segments still insist on the ancient theory of critical path being a single path, continuous from job start to job finish, a wrong mathematical assumption under resource leveling and multiple contractual constraints.

To make it worst, they create flawed theories about criticality, and go as far as including those flawed theories on forensic practice. Statistical methods usually will identify activities on the longest path with a high probability of becoming critical, but being critical or near critical is a different thing, usually close but not the same.

Would you say someone killed me because the bullet was close, even if the bullet did not touch me and I am still alive?