If the mind is physically independent of the material body but the physical world is closed, empirical observation of the material body cannot be sufficient to determine the existence of a mind.

Versus:

If the program is [abstractly] independent of the [particular] material computer but the physical world is closed, empirical observation of the material computer cannot be sufficient to determine the existence of a running program.

It's the [...] that hurts. "It is possible for one's mind to exist outside of one's material body." does not imply "the mind is physically independent of the material body". It's physically dependent and abstractly independent.