Love the original post and question.
To me, the behind the scenes stuff shouldn't affect things, but ultimately, it does. The easiest example I can give is Tateryche...err...Queensryche.
1981-1997, the original band wrote everything. Chris Degarmo was the main songwriter, who did the majority of the band's song arrangements, and split the lyrics and vocal melodies with Geoff Tate at probably a 60-40 percent clip in Chris' favor. And obviously, Chris came up with a lot of the riffs and harmonies. Michael Wilton was mostly a riff and solo man, and Scott Rockenfield and Eddie Jackson did their thing and got some credits along the way.
Once Degarmo left at the end of 1997, and Kelly Gray was brought on board, it was still Queensryche, but things shifted a bit. Tate wrote all the lyrics, and while Gray wrote just as much music as Chris did, on average, for the one studio album they did, things started to shift into Tate's favor. More like Tate directing what he wanted, music-wise, to want to write lyrics. But it WAS Queensryche to me, because Gray was a full fledged member of the band, and the band was a true band.
Once Gray left, and Degarmo returned a bit with Tribe in 2003, Tate continued to flex his controlling arm a bit more. Ultimately, one song aside, Tribe was the original lineup, but with reduced Degarmo contributions (three songs he wrote the music to, and two others that he made big contributions to...and then another song that he wrote entirely called Justified, which was released a few years later, but was intended for Tribe). Again, without that one track (Losing Myshit, which was written by replacement guitar player Mike Stone), Tribe IS Queensryche, albeit with shortened contribution from Degarmo.
After that, starting in 2006 with Mindcrime II, 2009's American Soldier, and the new record coming up this year, "Queensryche" has essentially become Geoff Tate's solo project. He directs everything. He chooses what music he wants to write over, he dictates the ebb and flow of everything. Other than a few things here and there, no one in the band writes music for the albums QR does these days. It's all outside folks (Jason Slater, and Kelly Gray, the latter who works for QR full time doing songwriting, recording, and front of house sound).
Once I learned how the whole thing post-Degarmo operated, I really got disgusted with the "band" (which is not really a band any more anyway). It has dramatically affected the way I view what gets released under the "Queensryche" name, because to me, it IS NOT Queensryche.
It's a frontman-led band very much in the vein of Whitesnake or Alice Cooper. The frontmen dictate the songs and what they want, and the players are interchangeable parts, with songs being written by whoever the frontman feels inspired by. That is ok if that is what the particular group is, and was started that way. But that wasn't what Queensryche ever was.
While QR has maintained four out of the original five members, the three remaining original musicians don't really write material Tate is inspired by, and so he looks outside of the band for songs, instead of accepting that this is where the musicians in the band are at, and utilizing their songs as "Queensryche."
When you accept all that, it is really hard for me to even listen to anything post-Degarmo and consider it Queensryche, because in all honesty, it isn't (although Q2k IS, it is almost an entirely different band, since the main music songwriter was Kelly Gray who is drastically different than Chris Degarmo...still, it IS Queensryche for all intents and purposes of this thread). But now, it's Geoff Tate's solo project featuring members of Queensryche.
And while that is alright for some, that isn't the band I was ga-ga over from 1987-2003.
So yes, the context in which music is created is very much an important part of how I evaluate and digest the music that I listen to. I like honesty in the music that I hear. I want truth. And to be very upfront...with that Queensryche example...had they ended the band after "Tribe," and Geoff did all this stuff under his own name, or a different band name, my opinion of the music probably wouldn't be any better, but my respect and appreciation for him following his muse as a solo artist would be there, whereas now, it is just disgust toward him and his Yoko-ish wife, because of the whoring out of the QR name to make a buck (which is what is going on).
It's unfortunate that outside things have an effect on appreciation for music and art. But for me, they do. It bothers me so much with Queensryche, that I've separated the original lineup's material from anything else released by the "band" on my iPod. I have it labeled "Queensryche" and then "Queensryche (non-original lineup)."
Anal retentive much? Probably.
But truth is truth.
So yes, the context in which something is created, whether it is the example I gave regarding who actually writes the songs, or the original post where the context talked about were the conditions regarding the recording, really does matter to me. It is that total package that really matters.