Ah, but this is not a personal philosophy, it is the philosophy of the art in question. Now, that can be passed down incompletely, or incorrectly, but not really in the way you're describing here.
Within Japanese systems, the way to ensure it is passed down completely and accurately is the Menkyo (licence) system. Menkyo Kaiden (licence of complete transmission) is, ideally, only awarded to those who completely learn the art (the philosophy) accurately and according to the way it is taught. Anything lower than that, and there is a real chance you're getting a flawed version of things. This is one of the main reasons that lineage is so important in Japanese (and Chinese) systems.
Ideally, if the philosophy is not in line with a particular student, they won't be students there long enough to gain such a licence. And if they do stay with it that long, then the philosophy of the art will be "trained" into them (really what the training is for, after all).
These days it's common for there to be many instructors of a particular system, from Shodan up, really, rather than just the person(s) who have achieved this complete transmission (that does still exist, though, such as in Katori Shinto Ryu, where only Otake Sensei was recognised as the teacher of the tradition for many years.... for the record, his son has now taken over his role as Shihan for the Ryu, and the Sugino Dojo seems to have been accepted back, or is at least being brought back in, as a branch dojo of the Ryu, headed by Sugino Yukihiro), leading to many people being taught an incomplete, or flawed version of the art. If you have seen the movie Kuro Obi (Black Belt), there is a great master of Karate, who is killed by the Army, leaving his three main disciples to go on. Each of the disciples has their own approach, one purely offensive, another very defensive, and a third pacifist, following the master's teachings. This is an example of incomplete transmission, as it ends with all three being spent, and only at the end coming to some understanding of what their master was trying to teach them at the dojo.
In terms of the philosophy of the art being flawed itself, well, that usually ends up as a very short lived martial art! Without a complete basis (philosophy, a guiding set of values and beliefs giving rise to the behaviours, or techniques and training methods), there will be no way to continue after the person who developed it passes. Often they have an internal congruent philosophy, but don't successfully manage to put that into their system, and that dooms it from the beginning.
Bear in mind, though, that none of this is really anything to do with the personality of the individuals learning it (although certain personalities will be drawn to, or repulsed from, certain specific philosophies, or arts). So the idea of "complete" to one person or another really doesn't enter into it.
So going on this, does this leave any room for changes in the art?