It's easy to assume that all metering nowadays works the way we want it to, because there's really no good excuse for it not to. However, there could be exceptions including well-intended ones (e.g. if the designer thinks, "no one can possibly hear a single-sample overload"). So it's worth loading the recorded waveforms into an editing program on a desktop computer and looking at the peaks in some detail. See whether they appear to run into some kind of limiting or not, or whether they seem unconstrained.
In live recording it is quite rare for signal peaks to remain uniform for any substantial length of time; when they do, it usually indicates some kind of electronic processing (limiting) along the way that is forcing them to fit a common peak amplitude. Whether that is occurring in your equipment or in some preceding equipment in the venue, you'll need to determine case by case. Some recorders and ADCs do, indeed, smash samples that come close to 0 dBFS--and sometimes you want that, at least for safety. But in live recording generally it's better to record first and process later, rather than to "bake" a certain kind and amount of processing into the only recording that you have.
With 16-bit recording, it's very rare that a recording venue is so quiet that you have to run very close to the limit. Typical real-world occurrences make that a dangerous practice; even if you get a run-through of a piece, the performance may easily be 2 - 3 dB louder than the rehearsal at some point or other. After years of analog live recording on open-reel tape, where the dynamic range was distinctly less than 16-bit digital and I got to be a bit of a hotshot at setting my levels so that they just went into the red briefly on peaks and came right back out again, the idea of crowding up against the absolute limit of a digital recording in a live situation makes no sense. If your peaks are anywhere in the top 6 dB without going over, count that as a complete success.
Again, I mean that advice for live recording. In dubbing or processing situations, with the live recording safely "in the can", then it does make sense to approach 0 dB closely IF you're sure of your metering. But that's a real IF. The PCM-F1, for example, had digital meters that were driven from a rectified, analog signal at the input, and they could under-read by as much as 4 - 5 dB in live recording situations; only the "PEAK" indicators were digitally driven, and even those didn't come on unless there were three or more consecutive overloaded samples. It was, after all, a consumer device even though pitched to advanced consumers. Many DAT recorders had similar metering.
--best regards