I'm still unsatisfied with your definitions because you're not separating the concept of the expression of a computation from the execution of that computation. A formalized process (read: language) is Turing complete if it can express the simulation of a Turing machine. Since we know a Turing machine can be used to compute anything that is computable, we then know our formalized process can compute all that is compute - it is Turing Complete.
Programs cannot be Turing complete. The concept does not apply, just as a basketball cannot be sad. Programming languages can be Turing complete. A robotic Lego "Turing machine" is not Turing complete, but not because it's not a realization of a Turing machine, but because it's not a formalized process. Robotic Legos, however, would be Turing complete, since that is the formal process used to simulate the Turing machine.
Programs cannot be Turing complete. The concept does not apply, just as a basketball cannot be sad. Programming languages can be Turing complete. A robotic Lego "Turing machine" is not Turing complete, but not because it's not a realization of a Turing machine, but because it's not a formalized process. Robotic Legos, however, would be Turing complete, since that is the formal process used to simulate the Turing machine.