In some cases students will need to unlearn techniques and ways of moving, but that is usually when they go from one art to another since various arts have different ways of moving, not just different techniques. Going from Tae Kwon Do to Tai Chi is a good example. I don't see the same thing with similar arts, such as various FMAs. Arnis, Eskrima, Kali, etc. are all similar enough that when someone learns the basics of one school they should be able to easily pick up another school's methods. Other arts are very compatible, such as Taijutsu and FMA.
It is a cliche in martial arts that it is better to start in a specific art with no training rather than having learned other arts. IMO this comes from people who are students and not teaching, or teachers who don't pay attention to their students. Most people who've taken one art and then another will remember having to change the way they do things, for me it was things like reverse punches and high kicks, for others it would be different things. What I've noticed as a teacher, however, is that it is better to know another art than nothing at all. While a student without any training will not have other training to get in the way, he will also not have any reference points. Students who know the way one art does things will see the differences and similarities in another art and will see the skills they are taught more completely than someone without a reference point.
With CQC it should be even less of an issue, since there are not specific styles of movement like in martial arts. I've taught SFC knife techniques and also things I've learned in FMA in a Taijutsu class and it had no negative effect on anyone.
That is actually a strange reaction for a knife instructor. At least most the knife and CQC people on the internet seem to want to learn as much as possible, not only one system, unless they are the "cult types" who think their chosen guru (used here as a cult, not FMA, term.) is the only one who knows anything about self-defense.
It could be that he doesn't want competition.