The pictures absolutely prove why it is always better to buy a belt drive machine. When one component failed, the other went with it. Usually when a flange fails like that it is an overspeed situation which caused excessive heat build up. I cannot blame Honda for wanting to examine the unit to see if it is their fault nor can I blame the pump manufacturer. All pump/ engine combinations are designed and built to run within a narrow range of performance values, to alter them leads to problems. Honda now insists on testing anything that has their engines attached for all performance factors like emmissions, vibration, heat etcetera.
We have sold thousands of 13 HP Honda units and have not experienced undue problems with reliability.
However, with the 20 HP units we did experience some interesting things: it appears they were originally built with splash lubrication then changed to pressurized; early run models had a plastic paddle inside that usually melted at ~300 hours siezing the motor. Honda eventually covered that under warranty. Another thing related to this engine is it is EXTREMELY sensitive to oil level in the crankcase. Moderate overfilling will cause blowback through the carb and eventually choke off the engine and requiring a non-warranty cleaning. Unlike the 11 and 13 HP units this engine in NOT equipped with an 'Oil Sentry' shut down, merely and oil alert; so make sure you check your oil level in this engine every time you start it and do not overfill.
Like any other product the warranty and after sale service is only as good as the person doing it. I know of a situation in Wisconsin where an end user could not get timely, accurate warranty service on their Kohler engine. The irony is he lives 20 miles (32 km) from the town of Kohler (World H/Q).
You never pay too much but you can pay too little. If you pay too little you can lose it all and need to retain some extra for just such an eventuality. If you can do that then you can afford to spend more. Like the Fram commercial; "Pay me now or pay me later." Remember that Rolex has a 90 day warranty, Rolls-Royce has less coverage than Hyundai; so quality never has to worry about warranty (if it is wrong it will be made right).
Cheers.