What is "true"?This is a very philosophical discussion, meaning there is probably not really a definitive answer, just an endless list of things to consider.
Also, it is a very serpentine discussion, meaning I'm not sure where to start, so I'll just pick a spot on the canvas and begin painting with broad strokes.
What is "true"?
By "true", most bands are referring to being true to 'their sound', how accurately they are portraying it, usually based on their live performances. They want to sound like they do live or, more accurately, what they want their live performances to sound like: the quality of sound of each instrument (such as a certain distortion on the guitar or an un-gated snare), the instrumentation (eg. guitar + bass + drums + vocals and nothing else!), and other qualifiers (feel, energy, tightness, etc.). There is a respectable amount of desire to make the recording as representative of the band's sound as possible, but even aside from agreeing on what is meant by "true" and "sound", there are a host of other things to consider.
Let us suppose we record some songs as you play them with the instruments you normally use to play them and the musicians with whom you normally play. Where do we put the microphones? Microphones are the ears of the studio recorder, and no one ever listens to a concert with their ear in the kick drum. And if they did, they could not very well have it in front of the guitar amplifier speaker at the same time. And up to the vocalist's mouth as well? (Or, rather than the vocalist's mouth, should that be the PA speaker, where the vocalist's voice is amplified to be heard over the band?) So, merely placing microphones on each instrument is a lie because we humans have (at best) two ears permanently affixed to an orb on our shoulders, making it impossible to place our ears in front of all these instruments in the manner microphones are placed.
And there's a time-space situation to be considered since a microphone next to a speaker hears the sound almost instantly, but a microphone across a large room will hear that same sound 18 milliseconds later, and that can greatly alter tone quality when blended with other sounds. Lies!
And different microphones have different frequency responses, missing out on some frequencies and accentuating others. Technically, this is not a true representation of the sound created, that is to say: Lies!
Let's overlook that for now. Do we put reverb on the voice? Compress the bass? EQ on the guitar? LIES! More lies!
Ok. So maybe "lies" is starting to sound a little heavy-handed. Let's call them "compromises" because what is most true is often not the most flattering. There's a reason snares get gated, voices get reverb, basses get compression, and so on. Our ears hear a wider dynamic and frequency range than most microphones and definitely more than most speakers, so the microphones are losing some of the information and the speakers are turning around and losing more.
And we haven't even discussed what happens when someone digitally compresses the audio.
Too, what will your audience be listening on? Bluetooth earbuds? Laptop speakers? Home stereo? Car stereo with road noise? All of those? Something else entirely? Whatever the answer, it affects the sound. ...and it is out of your control. So, whatever the truth -er- compromise was up til now, it's been filtered with the end listener's choice of playback device.
Too, I feel it worth mentioning that most albums I've recorded have been well-served by a nice tambourine track somewhere on the album even if the band doesn't have a tambourine player. We add it because it sounds nice, but it's technically a lie (in regard to representing the band's sound) since they don't have a tambourine player. But it's usually an acceptable lie, serving the greater good and all that. So, what about an extra acoustic guitar rhythm track to "beef up" the mix, even though the band doesn't use an acoustic guitar live. Should we double track the lead vocals? (Freddie Mercury, Eminem, Lynyrd Skynrd, Elton John) Perhaps bring in a vocal ringer come in to sing harmonies? (Shannon Hoon was not a member of GNR.) What about a keyboard track? (Billy Preston on the rooftop?)
My humble opinion.As Alan Moore says (through his character V), "Artists use lies to tell the truth."
The studio is for recording the platonic ideal of the song, whether it be something you can approximate in a live setting or not. My goal as an engineer is to go unnoticed in the final product. By extension, I think the goal of recording should be to sculpt a sonic product that conveys the song to the listener without drawing attention to the production. When you watch a movie, you should never think "that pan shot was shaky" or "the background action is distracting", rather you should think "How will they make it out of this situation?" or "Just kiss her, you fool!" To the extent your budget will allow, re-do the parts until you're happy. Use the sounds that please your ears. Modify as necessary to capture the essence of the song.
I have far from exhausted this topic, and, unless you really pin down the question, there really is no answer, but I hope this has given you something worthwhile to think about.