As BAS and myself have just pointed out, there is one phrase in that declaration which seems to imply that the person signing it has actually undertaken the tasks.That is the implication, it allows the person signing to oversee the functions, but not retrospectively - as expected by the OP.
However, as for bernard's point about "being responsible" (which is really also the basis of your comment), there is plenty of precedent for people been 'held responsible' not only retrospectively, but for things with which they have had no direct involvement at all - we see lots of sackings and resignations of directors, CEOs, ministers etc. because of their responsibility for the actions/inactions of those 'under them', even if they were not aware of the particular actions/inactions. Hence, if the declaration did not include then "when carrying out" bit, there might be a lot more scope for debate.
I wonder how a hypothetical 'court', or any part of officialdom, would view the situation if someone signed the declaration, 'taking responsibility' for the design, construction and I&T, but crossing out or modifying the "when carrying out" bit?
Kind Regards, John