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I don't know who runs it, but I've seen it quoted by writers as a source on other websites, but I don't remember any specific cases at the moment.  Its name usually is found hiding in footnotes, but not in the body of text or prominently featured in the title or sub-headings. Someone who doesn't read footnotes would likely miss it. Ironically, when one reads Catholic Candle articles, it is sometimes informative and interesting to read the footnotes FIRST, quickly, and when you see something you want more details on, then click the boxed arrow at the bottom of the footnote and it will take you immediately back to the point in the article footnoted. You might then find starting your reading of an article somewhere in the middle is the best place for YOU to begin.
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I have often thought that it is an SSPX layman or perhaps a group of priests who don't want to be identified (out of a reasonable concern for consequential reprimands) who are sometimes unhappy with the current state of affairs in various ways, such as laxity of the faithful, unwarranted pacifism of priests, lack of fight against the errors of Vat.II, weakness of the Menzingen leadership of the Society, GREC, and so on.  It even goes so far as to be critical of Bp. Williamson, associating him with the "False Resistance."
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https://catholiccandle.neocities.org/priests/williamson.html
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Not infrequently it seems to have been quickly translated from a French original, or else it is written by someone whose first language is French. Take for example the article on GREC from 2015:
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https://catholiccandle.neocities.org/priests/sspx-grec-hidden-story.html
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I highly doubt that its source is Fr. Francois Chazal, as he is much too busy to have time to put its content together, plus it doesn't read like his style. It must be someone who has access to various sources in the Church as well as time to spend compiling the material.
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Catholic (S)candle is run by a Pfeifferian lawyer out of Chicago.

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So that explains why there's never any words critical of Boston, KY in the Candle.
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Come to think of it, seems I saw a reference in The Recusant some months ago.
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It also would explain why the SSPX drills aversion to the Internet into the heads of their seminarians.
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That is, Bishop Fellay has something to fear in its pages.
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I doubt that +W has much concern though. He seems able to keep his head up regardless.
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On the Catholic Candle site one can find a 364 page PDF of a work called Lumen Gentium Annotated.  That does not even include 2 introductory pages plus a 28 page preface!  It's quite a work -- possibly the most extensive critique of Lumen Gentium ever. The work has a ton of footnotes and appears very well docuмented.  The site offers it as a free download while it can also be found on Amazon.  

The work appears to have been one of an anonymous author or authors as it simply attributes authorship to the "Editors of Quanta Cura Press."  I did an advanced search on the Internet for Quanta Cura Press and came up completely empty handed.  Hmmm?

Father Rafael Arizaga signs his name as it is supposed to be (Spanish) while the author of Catholic Candle changes his name using the English version, Raphael. ????

Moderator: the short answer -- "Catholic (S)candle is run by a Pfeifferian lawyer out of Chicago."

It is a scandal because they, being Pfeifferian cultists, love to attack faithful Bishops and [priests] such as Bishop Williamson, Bishop Zendejas, etc. and propagate the Pfeifferian propaganda that most of the Resistance is the "false resistance" and only Boston, KY and those uncritical of same are the "true resistance". Like I said, a cult.

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Is it fair to presume when you say "a cult" you're not talking about one like the cult of Mother Mary?
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Thank you, Matthew, for taking the time to post your assessment in so few words, and for allowing this thread to continue.
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Now, if only the spelling of "candle" could be changed to candal we could be making serious progress! But I digress.
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So much of what can be found online is conspicuously missing particular facts. It seems today's world is adapting to the power of search engines, to support a subtle agenda of concealing key data that would make research and consequent understanding so much more accessible. 
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While I agree that besmirching the reputations of good clerics is not a good thing, especially when it runs alongside the selective adulation of other clerics whose history may be objectively checkered, nonetheless, it behooves the Catholic looking for informed comprehension of reality to be able to identify important turning points in the story so it can be easily, calmly and clearly explained to others, in particular to adolescents, converts and children. We should all be capable of giving informed and honest answers to those who ask us honest questions without having to resort to hyperbole, platitudes and blanket statements.
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Don't you think?
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Most of neo-tradition is a cult of one type or another.  Extreme loyalties to this or that chosen personality is the style today, while the brotherhood founded on Christ's doctrine is hanging in some obscure closet.

 An entity which is not a church is in power, and even those who dissent from it, follow it in some measure breathing, in the trailing air which is devoid of God's authority and order.

Is it any wonder?