Iain Moncreiffe of that Ilk is correct. The 'common law' he is referring to for England dates to a legal judgement in 1321.
The Statute, however, dates to 1351 (not the fifteenth-century as claimed in your quote.)
So, a fourteenth-century statute, De Natis Ultra Mare, did restrict the English crown to those in the liegeance of the Sovereign. However, that statute replaced the earlier Common Law based on the judgement of Rex v. Philip de Beauvais in 1321.
The paragraph in your quote from Wikipedia seems to have been added to an an old version of the page on the Jacobite succession. It was added by an anonymous editor on 27 April 2009, but without citation. The entire section was subsequently removed, which is why it's no longer searchable, although the claim is now repeated on a number of other sites.
That is regrettable, since the paragraph is incorrect in every important respect!
However, I think the root of the problem here may actually lie in a misunderstanding of what constitutes Common Law, and how it differs from Statute Law.
I apologise in advance for the fact that what follows will, of necessity, involve a certain amount of 'legalese'.
Common Law is the part of English law that derives from custom-and-practice and judicial precedent (i.e. previous court rulings), rather than statutes passed by Parliament.
The principle that inheritance was limited to a person born in the liegeance of the Sovereign, or naturalised, dates to a case brought to the Eyre of London in 1321 (Rex v. Philip de Beauvais). The judgement in this case was that foreign-born persons were indeed excluded from inheritance (essentially because of the difficulty of proof), although the case hung upon the dual meaning of the word 'liegeance'.
Philip de Beauvais inherited an estate from his father. The king's Serjeant, Geoffrey Scrope, argued that Philip's father was born outside of the king's ligeance, or 'territories'.
"Votre piere ne fut nient de la ligaunce d'engleterre"
Now, in the early fourteenth century, English lands belonging to foreign-born individuals automatically became the property of the king upon the death of that individual.
The attorney for Philip, a Serjeant Shardlow, argued that Philip's grandparents had been married in England, paid homage to the King of England, and died in the king's homage. Therefore, although Philip's father had been born in a foreign country, he was nevertheless technically born within the king's ligeance or 'loyalty and obedience' (taking the alternative meaning of the word ligeance).
Although the judge initially ruled in Philip's favour, that ruling was overturned on appeal and Philip forfeited his inheritance to the king.
However, what matters here is that this judgement then became part of English Common Law. It also meant that titles (technically including the Crown) could not be inherited by a person who was not 'born in the liegeance of the Sovereign, nor naturalised'.
So, Iain Moncreiffe of that Ilk was entirely correct in his assertion about Common Law.
Now, Statutory Law in England were the laws passed by Parliament. Statutes often clarify and take precedence over Common Law.
The statute being referred to in this case is presumably De Natis ultra Mare (25 Edw. III Stat. 1) 1351. This Act superseded the earlier Common Law.
The text of the statute is available in Latin, with and English translation in The Statutes: Revised Edition, Vol I, Henry III to James II, A.D. 1235-6 - 1685, p175. The relevant portion states:
"... the law of the crown of England is, and always has been such that the children of the Kings of England, in whatsoever parts they be born, in England or elsewhere, be able and ought to bear the inheritance after the death of their ancestors; ..."
"... And in the right of other children born out of the ligeance of England in the time of our lord the King, ... shall be from henceforth able to have and enjoy their inheritance after the death of their ancestors, in all parts within the ligeance of England, as well as those that should be born within the same ligeance. And that all children ineritors which from henceforth shall be born without the ligeance of the king, whose fathers and mothers at the time of the birth be and shall be at the faith and ligeance of the King of England, shall have and enjoy the same benefits and advantages to have and bear the inheritance within the same ligeance, as the other inheritors aforesaid in time to come..."
So, while the quote is correct that a statute restricted the English crown to those in the liegeance of the Sovereign (although it was a 14th century statute, rather than a 15th century one as claimed in the quote), in fact that statute simply replaced the earlier Common Law judgement of Rex v. Philip de Beauvais in 1321.
There is an excellent course, from the University of London and available on the Coursera platform, that offers an Introduction to English Common Law if you're interested in following up on the topic in slightly greater detail.
As an aside, this little known part of English law is often claimed to have established the principle of jus sanguinis operating alongside the principle of jus soli, which in turn influenced Article II Section 1 of the U.S. Constitution which states:
No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.
- Adopted by the Philadelphia Convention on 17 September 1787.
(See, for example, Natural Law and Birthright Citizenship in Calvin's Case)