The bands that I listen to, when doing covers, they adapt it to their current sound, so I'm talking about my experience. What other reason could there be to do a cover if it's not to adapt some song that you like to your sound?
What about yours? Nin do covers? How do they sound? Like nin or do they change the it on purpose?
First of all, you do a cover because you like the original song - unless it's some PR shit, and the label forces you to do so, but nowadays I'd like to assume people are much smarter than to agree to anything. Anyway, this part doesn't matter in case of IF.
After that, you can think about how you want to do it. You don't have to go full out on a song to cover it. Metal covers are fucking boring, let's be honest here. These songs are less poppy than The Truth; think about that for a moment. No Good is exactly what a cover song should sound from In Flames today. Down in a Hole is somewhat lazy, and I won't ever listen to Wicked again, one was exactly one too many times.
What did you expect IF to sound like on POP SONG COVERS after Battles exactly? If we exist in the same reality, it's been a year since IF released Save Me. If anyone wants to pretend they are shocked what IF sounds like today, then at best they are 1 year late to the party. You have to draw a line eventually on how zealous you want to be exactly. My advice is not to give a flying fuck about covers in general. If you like it, grat. If you don't, too bad. All that matters is what they burn on their studio records.
As for NIN, he did not do many covers. My favorite is Dead Souls, but it is pretty identical to the original, he just sings in a different way - and to be fair, the singer of Joy Division had a very weird singing style - and shortened the intro. The one song he kinda converted to his own style back then was Get Down Make Love by Queen. An industrial synth-rock song about sex on an industrial synth record about - mostly - sex. Can't say he risked too much there, though it's impossible to listen to it in public because of the porn samples.
There is an unofficial hidden gem however, when it comes to NIN covers. Ladies and gentlemen, let me present you the 1 time Academy Awards and 2 times Grammy awards winner, father of four, mastermind behind the record The Downward Spiral, and surprise performer of the infamous Woodstuck '94, Mr. Trent Reznor!
On a more serious note, officially there were no cover songs on any record, only as bonus/hidden tracks. Only with the re-release of The Downward Spiral did Dead Souls was officially given a proper space on the record, years later. And yes, he did have a cover that did not really fit much onto the record, and while it was heavy, it was not at all on the level of the other songs.
FYI, this was a bonus track on the Broken EP, which had 4 proper songs on it, two of which won the Grammys, and one of those (Wish) is like top 5 famous songs of theirs. So yeah, if people were to be smartasses upon hearing Physical and saying shit like "weeeellll, I guess NIN is dead!!!!!!!!!!!!!!!! This cover blows!!!!!!!!!!!!!!!!!!!!!!!! Fuck NIN, man!!!!!!!!", then they would have been pretty fucking retarded.
Is this the performance you would expect after hearing Physical? No. You can judge covers, but you can't judge by covers.