It was a new sound for the scene, a lot of kid's wishing to express themselves but lacking in ability to do so quickly latched on. While emo started as an off shoot of hardcore it quickly became it's own beast and starting influencing other genres, even the ones that had influenced it in the first place. Pop-punk started seeing emo creep in, indie rock caught on, and even hardcore (resulting in screamo) eventually started incorporating emo tropes. The early 2000's is where emo really hit mainstream and branched off into something different.
The early 2000's is where emo broke mainstream and even those top 40 listening, pleb, mouth-breathers, knew the term. However this is also where it became something it never was. Bands like Brand New, Taking Back Sunday, and Jimmy Eat World hit mainstream success with lots of radio play. The term emo was applied to them due to their style and lyrical content and the radio-friendly scene having a limited vocabulary. At this point I don't really know of many actual emo bands still around, it pretty much turned into something all it's own that leaned more towards pop than emo which had leaned more towards hardcore.
This is also around the same time we got screamo. Which took emo's hardcore roots and focused on the aggressive side of things. It gets it's name from the fact that most of the lyrics were screamed (duh) often featuring two vocalists, one for the screaming and one for the clean vocals. Bands like Thursday, The Used, Silverstein, and Senses Fail were at the forefront of this style. Again even screamo saw radio play. This is also where the term emo got it's negative connotation. It can pretty much be traced to one band in particular, Hawthrone Heights. What most of the population saw/heard was whiny, angst ridden, teens. From that point emo became a way to describe any band with harsh vocals that wasn't metal and anyone wore those tight jeans and black shirts. True emo music was really no where to be found.
This also where bands like All Time Low, Mayday Parade, We The Kings, and Cute Is What We Aim For all hit the scene, all labeled as emo. Emo pretty much had evolved (or devolved depending on how you see it) to be the new pop. Most of the bands started to sound very samey, all trying to out lyric each other. Of course there were always stand out bands or albums that seemed to break the mold and be a bit more progressive. There were still bands that clearly leaned more towards hardcore rather than pop but really emo as it was, was dead.
Then we started to enter a new decade and emo started to come back. First many of the already established 'emo' bands started leaning less on being clever with lyrics and started branching out with style and sound. right around 2006 was when the scene started showing signs of change. My personal feelings aside, Brand New's The Devil And God Are Raging Inside Me, is a landmark album that really brought back a lot of the style and substance that had been lacking.
And this is where we start to see what people call the emo revival. Almost all of a sudden bands like Citizen, Title Fight, Basement, A Great Big Pile Of Leaves, Northenmost, and Into It.Over It, appeared on the scene recapturing the sound of emo in the early 90's. Basically return to it's original form. I actually thought Basement's Colourmeinkindness was an undiscovered album from the 90's until I found out it was from 2012. Even screamo has seen an influx of bands like Touche Amore and Pianos Become Teeth. If anything it's even bigger than when it began.
So back to the original question, is the emo revival fact or fiction? Really it depends on how you look at it. If you consider what the genre became in the early 2000's to still be emo then no, it's just a return to the original style. Personally I think the term revival is apt to describe what the industry and the genre is seeing. It evolved to the point where it really became something completely different, it really wasn't emo any more. I would actually apply the label emo to these bands. This emo revival is a fact.