agripper v. s'agripper

[alan gould]

When I questioned the need for the reflexive in "se tenir à une branche" I believe a French friend said it was to emphasize the clinging.  Likewise, I imagine, with "agripper."  Is the logic that when I initially grab the branch, there's no indication that I'm going to desperately hold onto it?  Therefore, that's "agripper."  But if I am hanging on to it, use the reflexive.                

agripper  - to grab, to clutch  

s’agripper à - to cling on to  

Elle s'agrippait à la branche.  She was clinging on to the branch.