I think the situation as to pronunciation as it exists today has been pretty well covered by your other answers.
But I wonder if you might have found information about this from a source that was thinking more in terms of long term history. Withycombe's The Oxford Dictionary of English Christian Names gives Meriel and Miriel as common alternative spellings of Muriel in medieval times, and says that the modern English surnames Merrell and Merrill sometimes derive from an ancestress named Muriel. This implies to me that back in medieval England the pronunciation of the first syllable of Muriel rhymed more with the modern word "fur" than it does with "pure". In other words, original Muriel didn't have that y-consonant sound in the first syllable that English speakers use today. Perhaps that somehow got into the name when it was revived in the 19th century.
And if back in medieval times some there were dialects where "ur" turned to "air", that would explain how the Merrill is related to Muriel.
Finally, in the dialect of most of the United States, Meriel and Mariel would today be pronounced about the same, just as most Americans west of New Jersey pronounce Mary, merry, and marry the same. So perhaps the idea that Mariel is ultimately a variation of Muriel comes from some American linking them through the medieval spelling Meriel? Just a thought. :)