The Santos-Dumont 14-bis [14th attempt, 2nd variant] 'flew' in September 1906...a flight of 23 feet; dismissed as a 'powered hop'. However; it still poses a tenuous claim to 'first'. Technically, the title of 'first heavier-than-air powered flight requires the aircraft to take-off from the ground without assistance, and the Wrights were using a drop-weight to drive a small trolley that the Flyer rested on. [ by the same reasoning, Langley's catapult attempt from a houseboat wouldn't have counted either, though his claim would be greatly strengthened if the 'aerodrome' had flown instead of taking a header into the Potomac River.]
It's hard to say if the Wrights dogged resistance to wheels lasted past September 1906 since they were doing little or no flying at the time. They were keeping everything under wraps until they locked up their patents. [also, they were pestered by a very curious, though disbelieving, press.] The Wright Brothers consistently come across as businessmen, first and foremost. In contrast to Europe, they show little sense of the joy-of-flying.
In any event, 23 ft. is a slender reed to support such a large 'First'. The early pioneers were drunk with the notion of flying, at least in Europe, and by 'flying', they did not mean 23 ft. They meant to soar like eagles. [ In fairness to Santos-Dumont, he did considerably longer flights in the suceeding months.] One historian posed a reasonable benchmark for 'first': namely, that the airplane should lift off under its own power, fly a quarter mile, do a controlled turn, fly back, turn again and land, i.e., fly a closed loop under control. So the Wrights claim is probably safe for a while yet.