To justify my position, I need to make two points
1. As a body of knowledge passed from person to person, Aikido isn't "self-correcting". For example, an instruction set on how to produce a specific origami shape is self-correcting in that if some of the instructions get garbled up, the result will be so obviously broken that the garbled instruction set will not be passed on to another person. (This example is from The Greatest Show on Earth by R. Dawkins, here is a relevant wikipedia link http://en.wikipedia.org/wiki/Memetics)
Aikido, generally speaking, is not self-correcting; a student may miss a detail from her teacher's demonstration and not pass it on to her student, another student may wilfully modify things (perhaps because the world has changed and the ethos needs to be adjusted to the new reality) and pass that on, etc...
I think that the first point is self evident, the second one may be less so
2. Aikido is martially effective. This is necessary but maybe not sufficient. Regardless of other things Aikido brings to the table (health benefits, world piece, etc...) it has to be effective. If it isn't, everything else collapses in a cloud of self delusion. Some people may disagree with this - I have no problem with that, we are simply don't have a common ground as we don't practice the same discipline. Some people may say that this effectivity business covers a lot of grey area. This may be true but does not imply that everything is as effective as anything else (http://www.youtube.com/watch?v=gEDaCIDvj6I
) For example if nage/tori exposes his back so it can be struck by the uke, he isn't practicing a martial art (http://www.youtube.com/watch?v=kWBmEHzbOXI
) but some sort of acrobatics.
I suppose that some might disagree, but this is how I think about these things.
So how would an Aikido practitioner, who accepts points one and two, think about assimilating influences from other martial arts?
As far as the first point is concerned, these introduce mutations to the body of knowledge that is likely to persist in future generations. This may or may not be a bad thing in itself but in the larger scheme of things it reduces the fidelity of the transmitted information.
Regarding the second point, most of us are salesmen, software engineers, nurses, mechanics and clerks with just enough free time on our hands to dabble in martial arts, maybe twice a week, maybe less. There is very little in our background to support a rational evaluation of martial effectiveness of this technique or that move.
For me, having accepted points one and two, proper training consists of following as closely as possible my teachers and being honest about my abilities to improve or change the art for the better.