I really find this interesting. I have just beening discussing this thread with a solicitor friend of mine, and they had a few interesting points.

They agreed that people should not be using the K-1 title AND LOGO, as this would then imply a commercial link.
As this has been an description of rules used for over 10yrs, it could be now classed as a generic term, just like the company hoover, and hoover the tool you use to clean carpets. I however could not copy the same hoover logo/written font and imply that I have attach myself with the hoover company.
I think we all agree with NOT using the logo. The term however is now generic and as no action has been taken to date, individual promoters could argue the case should it now come up. An important question is:
- Does K1 Corperation have global protection?

My friend suggested that as regular action is taken to moderate these pages, the key people at axkickboxing.com have probably had legal advice, and as such are probably doing the modification as part of a second-guessing/clean-break exercise, and therefore protecting themselves should such a situation come up.
And although this is a free-speaking forum, and the people typing their answers are responsible for their acions, the key-people at axkickboxing.com have an affliation.....so it is therefore probably easier for them to delete threads with K1 in the title, than risk being affliated should legal action be taken.

As K1-rules are essentially kickboxing over 3x3's, I would suggest just going back to calling it kickboxing, and then bouts can be matched:
O.R. - Oriental rules 3x3's
or
M.K.R. - Modified Kickboxing Rules 3x3's