A lot of survival guides give this method but there are several problems with it. The first is that it's usually presented as what to do if you are lost and starving. However if you read through the directions you will hopefully realize that it will take 1-2 weeks just to examine the roots, stem, leaves, and fruit of one plant and during that time you can't eat anything else as that brings too many variables into play so if you have a reaction you won't be able to tell which plant material caused it.
Second, have you ever tried to hold something in your mouth for fifteen minutes (actually thirty minutes total!) without swallowing anything, especially if you are really hungry?
Third it doesn't test more subtle but deadly poisons such as from pokeweed, many legumes, etc.
Fourth, many poisons are not "contact" poisons but must be consumed to cause injury. At the same there are many plants that contain contact poisons which are easily removed by cooking or other native preparation method.
Fifth, if you do find some unknown, "nontoxic" plant that passes these tests there's still a very good chance that all you do is fill your stomach with matter that you can not digest which can lead to other medical issues, of which "the runs" is the most benign. Imagine a stomach full of grass. Most (not all) grasses will pass these tests but your body can't get any useful nutrition from them. However, filling your stomach with grass can interfere with your ability to digest other nutritional foods if you find some.

Seriously folks, just forget about this method unless you have a platoon of disposable(!) troops on which to experiment. It's bad advice written by armchair experts.

-Blast