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The reason some will caution against grabbing them by the legs is because they can slip a tendon if you are doing it wrong. You cannot grab below the ankle (some people think "knee" but the backward bend in their leg is actually their ankle), you cannot grab just one leg, you cannot grab one leg in each hand etc. We grab firmly at or above the ankle, both legs in one hand, a finger between the legs to keep them from grating on one another. Done correctly the bird cannot thrash their legs and will not injure themselves (or you).
The reason I don't grab around or carry by the wings like I see some people do is because their wing bones are far more fragile than their leg bones. Over the wings, with the wings pinned to the body (sounds like what you say you do, Ledge) is safer but allows them to kick their feet around a lot, which usually ends up in me being injured instead. I don't use a net just because I hate untangling them from it once they are caught.