Yep, it sounds like you may be enjoying the exact fruits that the BF labor is designed to produce, in regard to those nicer sounding intervals across strings (I notice this when playing a perfect 5th across 3 strings). The system is baked in, but the effects and offset are arguably minimal. Guitars/basses can be factory made without the system and retrofitted for it - from my understanding, it mainly involves moving the nut closer to the first fret (for us, the zero fret closer to 1st) and subsequent offsets when setting intonation at the 12th or 7th frets, depending on string, but tuning the open strings normally. The thing is, those offsets are 1 cent - aka, one hundredth the pitch differentiation between one fret and the next, which is pretty minuscule, especially on bass. Aside from that, action and neck relief will play a part as well, since the further the string has to be bent down to meet a fret and where that fret is actually located relative to the midpoint and endpoint of the string will account for a number of cents one way or the other as well.
If I understand the system right, if you move the nut (0 fret) closer to the 1st fret, all the frets result in a pitch slightly flat of what it should be - by a very, very small amount. This helps offset for what I mentioned - the string going sharp as you press it down and it flexes and stretches to meet the fret, but another part of that flat pitch is offset by tuning the intonation to result in a slightly sharp pitch at the 7th or 12th fret. The underlying idea is that some intervals are more forgiving to our ears of not being exactly, bang-on pitch, and some are much less so... we rob from the former rich to give to the latter poor, in order to make a more pleasing overall result. But, in the end, we're talking about one or a couple of hundredths of a semitone, so you may not be able to tell with the naked ear whether a BF instrument is actually intonated with the BF offsets, or traditionally.
But aside from that, it just looks to me, and sounds like as well from a few of the convos I've had with fellow MTD users who don't understand the system well or just can't be bothered with it (or don't have a tuner that makes it easy enough to achieve), a number just choose to forego the BF intonation offsets and intonate traditionally. That theoretically should make the first half dozen or so frets a bit flat, but there are so many factors at play - is it significant? I can't say either way, just asking the question.