Does offer up send the shipping notification after the seller provides legitimate proof he sent it or does it send the shipping notification in the messages solely upon him "saying" he sent it?
OfferUp receives the shipping/tracking status from USPS (if/when the tracking number is scanned at the various logistical phases). OU does not "take the seller's word" on the status of the logistical phases. In fact, once the shipping label is issued to the seller, there is only a 3 day window to ship (unless the seller requests an extension). Otherwise, the transaction gets automatically cancelled and you receive a refund.
Your $$$ is safe in an OU escrow account, nor does the seller immediately get paid after you receive the item. If the seller is "jerking" you around and does not ship, you will get your money back from OU.
It's not the app. The app is used by sellers/buyers for it's ease of use and convenience. You seem to want things done "your way", which is your prerogative , but there are sellers that catch a "whiff" of what they consider as "attitude" and decide to renege on the shipping transaction, as the system is skewed to the buyer. Sellers want to use the app at their convenience as well.
I, for one, do not sell on OU because the shipping system is a hack job (not an understatement), even if it costs less than other apps.