Learn English – Why are certain competitions called a “Classic?”

It seems to be an acronym, like SCUBA:

S(ociety for) A(merican) B(aseball) R(esearch) + -metrics.

Source: dictionary.com

OED has a note

[The origin of the phrase has been the subject of numerous ingenious conjectures: see Brewer, Phrase and Fable, etc. A probable suggestion refers it to the circumstances recorded in quot. 1703; a less likely source has been suggested in quot. a1691.]

So they don't know the origin. The citations are:

[a1691 Baxter in Reliq. Baxt. i. i. (1696) 44 Thus when I was at Coventry the Religious part of my Neighbours at Kidderminster that would fain have lived quietly at home, were forced..to be gone, and to Coventry they came.
1703 Clarendon's Hist. Rebellion II. vi. 36 At Bromicham, a Town so generally wicked, that it had risen upon small parties of the Kings, and kill'd, or taken them Prisoners, and sent them to Coventry [then strongly held for the Parliament].]

Both quotations relate a physical sending to Coventry: in the first by driving out from Kidderminster (around 35 miles away); in the second by deporting prisoners there (also around 35 miles, if the place is now West Bromwich). They favour the second, which mirrors what you found in phrases.org.