@ 421C: I have to disagree with your first statement and partly with your second:
That part applies to G-registered aircraft.
...
"An aircraft" but not "G-registered aircraft" is mentioned and it directly refers to the licences concerned which are discussed in article 61:
Art 61 requires a licence from the state of registry for a public transport or aerial work flight. If the pilot has such a licence, then Art 61 is satisfied without reference to Art 62.
Art 62 describes the conditions for a foreign licence to be "deemed to be a licence rendered valid under this Order". It is
not necessary for a foreign licence to be rendered valid in order to fly a foreign-registered aircraft, only to fly a G-registered aircraft.