I'm not sure this is true. I am pretty certain that the UK does not have unrestricted birthright citizenship as we do here. FWIW, Wikipedia says that to qualify, a child born in the UK must have one parent who is either a citizen, or is "settled" in the UK. It goes on to say that
Settled' status usually means the parent is resident in the UK or a
British Overseas Territory and has the
right of abode (or similar status), or holds
Indefinite Leave to Remain (ILR), or is the citizen of an EU/EEA country and has permanent residence, or otherwise unrestricted by immigration laws to remain in the UK or that Overseas Territory.
Maybe Claudio or his wife had "Settled" status while he played over there and Jr. is a citizen and has or could get a passport. But do we know that? For all I know Claudio had a temporary work visa and had to leave the country once he no longer was employed as a footballer in the UK (ie he did not have indefinite right of residency).