I stated in an earlier post (and perhaps somewhere in the archives, even earlier posts)that I thought gaijin was just a shortened form of gaikokujin, but strangely enough, after reading this thread and a few posts in particular about how gaijin had much deeper and culturally centered meanings, and then hearing it used in context (I'd been listening for it following this topic and also tried to think back to previous instances) I did notice that it sometimes carries a noticably different connotation than gaikokujin. I would have to agree that, while by and large it may be used in spirit as a shortened form, or at least, with no more harm intended, than 'gaikokujin', it does (quite quickly and fludily) shift meanings from foreigner to 'outsider' sometimes. The nuance is slight, but I sense a definite differentiation with how it is used.
In short, (and this is just my opinion) there are some things which the Japanese consider beyond the immediate reach of (but attainable for) foreigners; things such as perhaps linguistic abilities or the ability to assimilate along cultural lines such as cuisine, acclimatization to Japanese style apartments, lifestyle, etc., But for much deeper and sacred cultural dealings, there is a sense that some things will just never be understood or fully appreciated by foreigners. I can't pinpoint them, as these kinds of things are always apt to be a little more subjectively treated, but I'd imagine they may include things like tatemae, using keigo properly, various ceremonies and forms of unspoken but culturally rooted conduct, etc. When it comes time for these topics vs. the more mundane and every-day, I feel gaijin is invoked moreso than 'gaikokujin', laying down the groundwork for a slightly different separation from native Japanese. Something more concrete and final, hence a little more unattainable.
Breaking through these barriers would not be impossible, but I think it'd be more of a one-on-one, case-by-case situation rather than general accetpance. That is to say, proving your un-gaikokujin-ness is easier than proving your un-gaijin-ness.