"Anything that can operate outside the context of a Turing machine can usurp said machine."
If the operation allows it to modify the instructions of the Turing machine then obviously, just by replacing the instructions with a different set. If the operation allows it to modify the input tape of the Turing machine then the same statement can hold in a strict sense: print your program a long way away from the input on the Turing machine and the machine won't see it, so it won't be erased or run. Otherwise it's an obvious no for an arbitrary machine: the machine that does nothing at all is a perfectly good machine, and cannot be hacked.
If you want to force the Turing machine to run arbitrary code, then we'll need a universal Turing machine for that, rather than a Turing machine. Then if you modify the tape, of course you are modifying the program as run into the machine's memory, so again you can do whatever you want.
But if you leave the program alone and just alter the input then no, you cannot force an arbitrary Turing machine to do your bidding.