I'm not a sound engineer so don't know exactly how it works, but I assume they take the original analogue reel-to-reel master tape and transfer that to a digital master tape.
They don't touch the original multi-track tapes, so there's no remixing of the tracks involved at all*. They are simply transferring an analogue master to a digital one.
I think how they do that process, though, does have an effect on the final sound - whether there is equalization, compression, reverb or whatever added onto the master tapes will change the way that master tape sounds**.
In the case of Pepper, they were taking an analogue master tape that was 20 years old and transferring that to digital tape, with the knowledge that it would be heard on CD and improved modern sound systems rather than vinyl and old turntables that were around in the 60s. So they will have changed the EQ settings to account for that.
The master tape they used to create your 1987 vinyl copy is the same new digital master they used for the CD, so with your LP it is a different listening experience than if you were using any of the vinyl issues from the previous 20 years. Modern turntables, hi-fi systems and speakers are vastly improved from the 60s so they are trying to give you a CD-like sound from the new vinyl version. And they aren't telling porkies when they say your copy is "digitally re-mastered".
I doubt I would even notice a difference if I compared the 1967 stereo vinyl copy to your 1987 copy, but many people with better ears than me say the original analogue masters sound better than the 1987 digital ones.
The whole re-mastering process was done again in 2009, but they took a lot more time over it and used all the new technology that had been introduced in the intervening 20 years or so. People with ears (
) seem to like the 2009 remasters. Even I can tell a difference!
Hope that helps.
*In 1987 they DID remix two albums - Help and Rubber Soul - because they didn't like the original stereo mixes on the master tapes which had vocals on one side and instruments on the other. They did a remix so that the vocals were more to the centre. That is why the 2009 remasters of those two albums contain both the 1965 mixes and the 1987 mixes on one CD.
**When Capitol Records in the States got some of the earlier Beatles master tapes sent over in the '60s they didn't just press them as they were, they made new masters and added reverb as part of the process. The remastering programme was overseen by Capitol producer Dave Dexter Jr, and those US versions are now said to have been "Dexterised"! (http://en.wikipedia.org/wiki/Dave_Dexter,_Jr.#The_Beatles
). These mixes are available on the Capitol Albums box sets.