Someone with more knowledge of internals will have to confirm, but I bet that the assignment is being processed before the conditional. As a result, the evaluation goes from left to right, thus making the last assignment (the one in the "false" portion) be the one that sticks.

The ternary operator gets its power from being able to embed it as part of a larger statment, not just in using it as an obscure if statement. Here's a better way to write that code:

$param2 = @_ ? "Shift" : shift;
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The ternary operator will return the value passed from whichever argument was run. You want to avoid side-effects in these arguments.