I'm not dreaming - these are great CD copies

I have an out of town friend who's given me some CD-Rs that he's made by simply copying music off of red book CDs. The music quality is extremely good - better than I'm used to hearing from my red book CDs. He's not an audiophile and has no idea what format is being utilized e.g. Lossless, etc.
Question - Can you really improve the quality of music from a red book CD by simply copying to some other format? If so, I'm boxing up all 300 of my CDs and asking my friend to copy make copies for me.
You will find others who agree that some copied CDs can sound much better than original.
It isn't some other format - it is the burning process that can lead to better results. The store-bought copies are stamped which, apparently, isn't always as good as burning. I have noticed this phenomenon several times but it seems it doesn't hold for all cases(?).

It is my opinion the reason that "burned" CD's sound "better" is that some of the high frequencies are lost during the process, thereby removing some of the CD glare in playback on some systems which have a bright sonic characteristic.

My hypothesis could be checked out if one is fortunate enough to have access to a dual sweep oscilloscope.
When analog material is copied to tape there is a loss of high frequency material and an increase in noise floor with each subsequent generation away from the original master.

Digital copying is different. It will not change the high frequency response or SN ratio. Each digital data point includes all the frequencies and you can't change the frequency response and still have the same data point. (A CDR copy will have the same file checksum as the original CD. If you don't have the same checksum, you have a corrupt copy. It is extremely unlikely that corruption would affect only high frequencies; you're far more likely to have skips, clicks and pops from corrupted data.)

If a CDR does sound different, it is probably due to a difference in how a player reads a CD. Commercially pressed CDs have the lands and pits physically pressed into the surface of the CD while CDRs have a dye coating that is physically burned to create lands and pits. Generally a CDR is only about 70% as reflective as a CD and there are a number of different dye formulations that can be used. Any audible difference with a particular player is more likely tied to this issue than anything else.
What Mlsstl said.
I have noticed that some copies friends have made me sound unexpectedly good, although I don't have the origina; to compare to.
I think one thing to keep in mind is that all signals are analog; digital is simply a concept to analyze analog signals that vary between 2 discreet volotages. The way I see it, ost of the signal is in these 2-voltages, but when it comes to picky audio aplications, all the other noise on the signal, variations from the 2 voltagews, timing errors, and whatever else can cause audible problems.
Truthfully, I didn't understand the last two posts.

All I know is that when I play the CD-R, the music is clean, with more detail and dynamics. And it's not my imagination.
Dumb question: what is a "red book" CD? Thanks!
"REd book" cd = the standard cd protocol (you know, 44.1kHz /16 bits, the works).