landshark, you ask many good questions. Some of them are technical while others seem more existential, but they're still good questions in my book.
One of your more existential questions was, in essence, "Why do equipment manufacturers sell us things that don't work together as we expect them to?" It's important to realize that just because "they" sell us stuff that looks all proper and well-packaged, we must still maintain some caution and know the limits of the equipment we work with. A microphone's or recorder's level of sonic quality may be one thing; its compatibility with some other given piece of equipment under specific circumstances may be something else again.
To zoom in on one particular situation that may well be affecting you now: Your Korg MR-1 recorder's mike inputs have a specified maximum signal level of -27 dBV. That's only about 45 mV, and it means that regardless of gain settings or meter readings, most good microphones not only can, but WILL overload the circuitry at the microphone inputs if you try to record loud sounds. A typical studio condenser microphone puts out 45 mV at sound pressure levels somewhere in the 85 - 90 decibel range. But 100 dB sound pressure levels are common in live recording situations, and your equipment must handle them without overloading.
Confirming the fear you expressed, unfortunately: Your recorder's level meters almost certainly read the signals at the unit's internal analog-to-digital converter--after the built-in mike preamp circuitry has already distorted them. It's that mike preamp (input) circuit which has the low overload threshold; it seems designed for use only with dynamic microphones, or low-voltage electret condensers whose sensitivity is no greater than typical dynamic microphones. That all seems rather 1970s-ish, to those of us who were around then.
The point is, though, that the overload occurs at the first active circuit stage which your signals "see," while the level meters are attached only to a much later stage of the recorder's circuitry. Thus those meters can't be relied upon to tell you when (or whether) an input overload problem is occurring.
(In case it's any consolation, plenty of other equipment has similar problems. Many professional microphone preamps have overload indicators which monitor only the final stages of the circuit--while their input circuits may have a low enough overload point that with the gain turned down, the output stage can do just what your recorder was apparently doing: cleanly amplifying a signal that was already "clipped" at the input of the same device. If the input signals are "hot" enough, such preamps can merrily pump out 25% THD, as I have actually measured, without the "clip" light ever coming on.)
The immediate remedies for this situation would probably be either (a) resistive attenuators ("pads") at the mike inputs of the recorder, or (b) connecting the microphones to a mike preamp which would boost their signals to (consumer) line levels, then feeding those signals into the line inputs of the recorder. If you choose the latter approach, be aware that the line inputs have an overload limit of their own (ca. 2 Volts), so any mike preamp used for this purpose shouldn't be driven too hard--professional mike preamps usually can put out 10 Volts or more.
Unfortunately the equipment manufacturers always leave you with some "homework" to be done before an important recording, and it does involve a little arithmetic with decibels and Volts, but it's easy enough to learn and there are always people who will be glad to help you. At a minimum you always need to know the sound levels you expect to encounter, the sensitivity of your microphones, and the input overload limits of your preamps or mike inputs.
And again in case it's any consolation, when I started recording percussion ensembles 25 years ago and again about 10 years ago when I started making relatively close-up recordings of highly trained opera singers, I had to replace a certain amount of equipment and find workarounds for problems that I never suspected I had, as a result of the dynamic range which those recordings demanded. Typical consumer recordings--children's birthday parties, office meetings, etc.--don't demand so much dynamic range especially at the high-intensity end of the scale, and most budget-priced equipment isn't designed to handle it, especially when sensitive microphones are being used.
--best regards
P.S.: I almost hate to say this, but it is true that microphones themselves can overload, as others in this thread have mentioned. With condenser microphones this is particularly a risk if they aren't correctly powered. Overload at the mike input stage of a preamp, mixer or recorder is far more common, especially when high-quality condenser microphones are being used to record loud sounds; still, there's some possibility that clearing up one problem along the "chain" will uncover the existence of another one.