Here's my thoughts.
I definitely see how Initiation paperwork can be lost or not mailed in at all. This can make it very difficult when chapters have situations like my chapter where Initiation is a couple of weeks before elections. That means when school starts back in January, you are dealing with a whole new set of officers. Hopefully, the advisors are keeping track just in case HQ doesn't realize that the paperwork wasn't received.
I don't know if it's the same process for all 26 NPC groups, but some may have where the transferee has to apply to be accepted as a member of the new chapter and the new chapter votes. For whatever reason the new group can't/won't accept the member. That doesn't mean that the member can't wear her/his letters. It means they are an alumna/alumni/however it's spelled for guys
. Be active as such. There may be others on campus in the same situation.
I too am tired of newbies posting and the same ole GCers jump on them. Give them enough rope until they hang themselves; it won't take long if they are not on the up-and-up.