There is a very logical explanation about why the WTBTS will never admit to a mistake, and ask for forgiveness from its followers. That reason is the whole disfellowshipping /disassociation/shunning doctrine that is part and parcel to the entire existence of this cult. Here is a section of the "announcement" with a different "error" inserted, and from a follower rather than the leadership.
Dear Elder Body,
It has been brought to my attention that certain brothers have had questions regarding my blood transfusion during surgery after a nearly fatal window-washing accident. Rest assured that I NO LONGER consume blood. It was only in my undaunted zeal to proclaim the good news to "All Nations" (as was Jesus' admonition), in these critical last days, that I allowed myself to receive this life saving treatment. It is regrettable that some have been stumbled by this treatment, likening it to desecrating the life force itself. This is NOT THE CASE! Being as I am, an imperfect human, I may have made an error in my thinking on the matter. It was my only hope that this life saving medical treatment might show the nations, and their governments, that Jehovahs Organization is not a harmful 'cult' as false media reports have caused some to believe, but that we are a loving organization with only positive motives. Again, in my zealousness to further the Kingdom preaching work I mistakenly had hoped to extend my life so that I could continue our life saving work. We do well to remember that Jesus was the only perfect person to walk the earth, and as well meaning as we may have been in this matter to expand the work He commissioned, we are confident that our merciful God Jehovah, who sees "all things', would take note of our intentions, and forgive us our "mistakes". It is my hope that this will satisfy any further inquiries into this matter, and that we may move forward in the ministry in glorious praise to our Heavenly Father.
Your Brother,
This is the kind of thing that could easily be used against them in a way that would cause them to lose all control over their masses. It is the real reason they will go so far as to admit that that humans are imperfect and make mistakes, but never as far as admitting an actual mistake.
Shoshana