It looks like the synthesis of those two seemingly contradictory things is:
If Congress is still in session after the 10 day grace period for the president to sign it has passed, the bill is treated as signed and becomes law. However if the 10 day grace period goes by and Congress is no longer in session at the end of that period, the bill is treated as vetoed.
Another approach:
Does nibbling on it count as a signature?
It looks like the synthesis of those two seemingly contradictory things is: If Congress is still in session after the 10 day grace period for the president to sign it has passed, the bill is treated as signed and becomes law. However if the 10 day grace period goes by and Congress is no longer in session at the end of that period, the bill is treated as vetoed.
Another approach: Does nibbling on it count as a signature?
Gonna have to pass that one to the Supreme Court. Does the sitting president have a Yacht the justices could borrow for a week or so?