These are not mutually exclusive statements. It probably can survive for weeks in rare cases, but if it doesn't do that often it doesn't matter.
Any method of transmission that infects fewer than one additional person on average are effectively negligible on the overall exponential curve.
So yes, it is likely possible that symptomatic people can infect others, and it is likely possible that a contaminated doorknob can infect people for a week, but if these things happen rarely enough, it doesn't matter. The virus will die out if other routes of infection (e.g. the more typical person to person transmission) can also be made rare enough.
Any method of transmission that infects fewer than one additional person on average are effectively negligible on the overall exponential curve.
So yes, it is likely possible that symptomatic people can infect others, and it is likely possible that a contaminated doorknob can infect people for a week, but if these things happen rarely enough, it doesn't matter. The virus will die out if other routes of infection (e.g. the more typical person to person transmission) can also be made rare enough.