my head-baffled stage lip / stack recordings, I've often felt the high frequencies sound overemphasized even with EQ to undo the boosts based on the idealized graphs. I figured sound engineers at shows were assuming everybody was wearing earplugs and boosted the highs to compensate.
There may be all kinds of things going on, situations are all different, and so the ideal response from the microphone is going to change along with that. The native response of the mic is very rarely the ideal response for the end recording, and that's why careful EQ is so useful. The best we can hope for is a good starting point which can be manipulated into what we want.
When farther away, we generally need more high-frequency boost to compensate for distance, which is what "diffuse field equalized" means - the microphone has somewhat of a high frequency boost built-in to it's native response. EQ can do the same thing afterwards, pretty much (see below). Sometimes a recording made at a distance will benefit from a low-bass boost too, but that's a different issue, and since every situation is different, there is no knowing if you'll need a boost or a cut, or what shape it should be. Generally though, when up close you'd want to start from a flatter response, and when farther away you want to start with a diffuse field type response with a bit of a high frequency boost.
Yet the exact amount is always going to vary. Some times the sound engineer is over-boosting certain frequency ranges, or doing the opposite. I guarantee I can make these mics sound muffled with zero high frequency content at all with EQ, just like I can make them shrill and over-bright sounding, or sound just right like I want it to sound.
Again, the native response of the microphone is simply the starting point. I'd suggest you try boosting and cutting by ear, first with a broad wide curve (low 'Q') to get things sounding close to right, and then maybe use an additional narrow (higher 'Q') filter to sweep around and find then cut whatever narrow range are hearing as being "overemphasized". I bet it is probably a rather narrow resonance range that is bothering your ear, and not so much the broad, shelf-like response. Work by ear to get things sounding natural and correct, rather than working by eye to try and dial in a curve which specifically reverses the native mic response curve in search of flatness.
Working that way, a diffuse-equalized native response with a somewhat boosted treble can have another advantage with miniature mics which often don't have a particularly low self-noise floor. If the native response imparts increased sensitivity at high frequencies, which causes you to cut some high-frequencies to get things sounding right, you will also be reducing the level of high frequency noise and hiss from the microphone itself at the same time, essentially making the background of the recording sound quieter than it would have if the mic had a flatter response. Likewise, if you simply do not need to boost that range as much as you would otherwise, you won't be boosting the noise as much either.
It's nice to have a native response which is close to what we want to start with, but far more interested in a response which I can manipulate to whatever I want easily without problems, and that usually means a relatively smooth response without narrow resonances, even if it is not particularly flat.