"They are not talking about metal flashing here. Your Tyvex or tar paper would be the water resistant material used to flash. And of course better to wrap the whole building and not just the corners. I have seen a few where they just nailed to the OSB which is a bad idea."
Although this is probably splitting hairs for a shed, neither 'tar paper' not 'housewrap' is considered flashing
under any building code.
In fact, housewraps like Tyvek only qualify as 'air barriers' in most cases...and not 'moisture barriers'
That said, I would go with the manufacturer's installation instructions, which is going to determine your warranty, and install true flashing like aluminum under the outside vinyl siding corners.
Otherwise you can find yourself SOL if you have a problem.
The few extra bucks spent is well worth the additional peace of mind.