There's nothing wrong with Fram, Purflux, or indeed Mann filters. The Fram and Purflux do look identical to the genuine Honda part, including the rather unusual seal.
I do not know of any car maker that actually make their own filters (or spark plugs, alternators etc.) but having worked in first tier suppliers, often with a satellite factory attached to car maker plant to feed parts in directly I do know about the quality control that car makers demand from suppliers. The parts for one car maker may or may not go down same production line as those for sale to others through motor factors etc. The difference is that as part of their QC car makers will generally take a random sample from batches supplied and test them, and also cut them open to make sure all is as it should be - and if it is not stiff penalties apply and the whole shipment will be rejected which causes major problems with 'Just in time' deliveries as the supplier has to rectify any problem, convince the car maker QC that the problem has been rectified (and procedures put in place to ensure it cannot happen again) and for a repeat offence the supplier can lose their hard earned and cherished preferred quality assured supplier rating - which in some cases can mean redundancies and plant closures. Honda and Toyota were our most picky customers but were fair to deal with, the BMW Mini plant at Cowley were the harshest, and would invoke their penalty clauses in the blink of an eye (£250,000 for every hour you failed to deliver parts if it caused a stoppage of their production line), the problem is in these days of just in time production (the clue is in the name) the car makers keeps no buffer stock and the supplier keeps the minimum they can, and if your parts get rejected the stock at both the supplier and car plant are suspect and all have to be 100% inspected (at supplier cost) before use.
So the difference between an OEM part and a generic part is mainly in the level of quality control applied, and the loss of a entire car companies business ( maybe worldwide) weighs heavily on suppliers, if you supply parts to car motor factors and the general public you may get isolated complaints, but believe me OE suppliers 'sh!t themselves when car a maker sends a team in for inspections and get suicidal when they ship bad parts and go through the wringer of inspections and audits and maybe big expense and potential loss of business.