Is a physical process with unbounded input Turing equivalent?
No.  You can't just sweep everything under the rug like that.  The answer depends on what model of reality / physics you subscribe to.

If your model of reality is continuous (e.g., Newtonian physics), then it's not necessarily true that that every physical machine is computable by a TM.  TM's are discrete, not continuous; if physics is actually continuous, then your assumption is probably not correct.  (It might be true that the outcome of a process can be computed to an arbitrary degree of accuracy by a TM, but that's a subtly different statement.  TM's compute discrete values, not continuous values.)

If your model of reality is discrete and finite, then it might be true that that every physical machine is computable by a TM.  But now the number of states is not unbounded.

You can't have it both ways.  Or, to put it another way, you can't just assume things without justification.