The "traditional" story, as based on Sir Thomas More:
John Greene was sent, in 1483, by King Richard III as a messenger bearing a letter from the King to Sir Robert Brackenbury who was then the keeper of the Tower of London. In this letter the King gave orders that his two nephews, "the little Princes in the Tower," should be put to death. Although this inquitous command was later obeyed by another governor of the Tower, Sir Robert refused to commit murder at his sovereign's behest, and sent his message of refusal back to the King by John Greene. It is a tradition that when King Henry VII came to the throne he bore enmity to this John Greene because he had played (only) the part of a messenger for Richard III in the later's wicked designs, and that John Greene fled from England lest he be captured by the King. It is said that "John the Fugitive" returned to England and for safety assumed the name of John Clarke. . . Despite his change of name, the identity of John Greene, the Fugitive was discovered, and he again fled from England, his further history being unknown.
There are a number of problems with this, not least that More was hardly an eyewitness and got most of his information about the reign of Richard III from one of Richard's most virulent enemies: John Morton, Bishop of Ely, Archbishop of Canterbury, Lord Chancellor of England, Cardinal - and inventor of the sleazy bit of logic known as "Morton's Fork".
There is no evidence that Richard III ever ordered the murder of his nephews by any hand or at any time whatsoever. He is not even the only suspect with access to the Tower and the staff thereof in 1483 - Henry Stafford, Duke of Buckingham also had such access. Buckingham had his own motives to kill the Princes, having a claim of his own to the throne equivalent to that of Henry Tudor, depending on one's view of the legitimacy of the Beaufort line. According to a manuscript discovered in the early 1980s in the College of Arms collection, the Princes were murdered "be [by] the vise" of the Duke of Buckingham. There is some argument over whether "vise" means "advice" or "devise".[4] According to this perspective, if Buckingham killed the Princes and blamed Richard, he could form a rebellion, putting the throne into play with only Henry Tudor as a rival. Indeed, he was one of the leaders of a rebellion, ostensibly in favor of Henry Tudor, in October 1483. However, the rebellion was quickly crushed and Buckingham executed. Henry Tudor would succeed in defeating Richard III two years later. (Adapted from Wikipedia.)
Henry VII, of course, had the best motive of all for wanting the Princes out of the way: their claim, if they were still alive after August 1485, was miles better than his.
So if John Greene was never King Richard's messenger boy in a murder plot, what '''did''' Henry VII have against him?
Maybe he simply Knew Too Much.
People who Knew Too Much under the Tudors, particularly Henry VII and VIII, tended to get "disappeared" or to be executed on flimsy or even trumped-up charges.
The execution of Sir James Tyrell, on 6 May 1502, must have been a red flag to anyone else who Knew Too Much - Tyrell "confessed" under torture to the murder of the Princes, but his real crime was supporting the rival claim of Edmund de la Pole, and aiding and abetting Edmund's escape to the Continent where Henry VII could not get at him.
It seems to have been about then that John Greene absconded - the timing is quite suggestive. Was he also a Pole supporter?
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There is also no particular reason to think that John "The Fugitive" was the John Greene who was the first husband of Edith, Viscountess Latimer. That must have been quite a brief marriage, as she was having children by her second husband, John Mordaunt, starting circa 1474 (or 1480 at latest) - and John "The Fugitive" supposedly had a pair of twin girls by his (first) wife in 1475.
Divorce was not allowed, but annulment was - the commonest reason, and the most thoroughly abused, was "consanguinity".
(Wikipedia) Under Roman civil law, which early canon law of the Catholic Church followed, couples were forbidden to marry if they were within four degrees of consanguinity.[5] In the ninth century the church had set the number of prohibited degrees at seven. In 1215 the Fourth Lateran Council made what they believed was a necessary change to canon law reducing the number of prohibited degrees of consanguinity from seven back to four.[6] The method of calculating prohibited degrees was changed also.[7] Instead of the former practice of counting up to the common ancestor then down to the proposed spouse, the new law computed consanguinity by counting back to the common ancestor.[7] In the Roman Catholic Church, unknowingly marrying a closely consanguineous blood relative was grounds for an annulment, but during the eleventh and twelfth centuries dispensations were granted with increasing frequency due to the thousands of persons encompassed in the prohibition at seven degrees and the hardships this posed for finding potential spouses.[8] After 1215 the general rule was that while fourth cousins could marry without dispensation, generally the need for dispensations was greatly reduced.[8] In fourteenth century England, for example, papal dispensations for annulments due to consanguinity (and affinity) were relatively few.[9]
Historically, some European nobles cited a close degree of consanguinity when they required convenient grounds for divorce, especially in contexts where religious doctrine forbade the voluntary dissolution of an unhappy or childless marriage.[13] (end Wikipedia)
"Consanguinity" also included relatives by marriage - canon law made no distinction between blood relatives and in-laws, which complicated things enormously.
So, if Edith, Viscountess Latimer ''was'' the first wife of John "The Fugitive", the marriage must have been annulled - and there should be a record of that somewhere.
The alternative is that the link between them is spurious - she was married to a different "John Greene" who died in the early 1470's, and John "The Fugitive" had a different first wife who died before 1488. (Spurious links are an all too common hazard of genealogy.)