I understand that honesty and integrity is a lot more complicated that the trite Sunday School lesson about being honest in all your dealings. One quote out of thousands available, should be sufficient --
"In matters of honesty, there are no shortcuts; no little white lies, or big black lies, only the simple, honest truth spoken in total candor... ” - Gordon B. Hinckley
Being a gay Mormon is a nearly constant dilemma of honesty and integrity. Personally, I have found that honesty is much healthier than dishonesty and so I try to stay on that path except when the price of honesty is more painful for someone I love than the price of dishonesty is painful for me (not an easy or necessarily healthy thing in and of itself).
Organizations and Corporations (speaking specifically of a certain Corp of the President) however, are much more immune to the ill health effects of dishonesty. Because organizations are not living breathing emotional beings they are not harmed by dishonesty in the personal way a human being is harmed by dishonesty. Poetically however, dishonesty usually catches up to the organization and can sometimes bring it tumbling down (ie: Enron, etc.).
Over many years, in fact from it's very beginning, "Lying for the Lord" has been such an inbred core belief in the Mormon church that in an era of the internet, Wiki-leaks, and expectations for greater transparency in corporate governance, dishonesty is becoming a trademark of Mormonism that threatens to undermine the otherwise good works of the organization. "Lying for the Lord" has many connotations that I won't get into here but you can find them online. Here I only use the phrase to mean it's least damning implication, which is something on the order of "saying what the church authorities believe the listener should hear rather than clearly stating the truth". This type of "Lying for the Lord" intentionality creates a fog around certain doctrines and points of history that the church prefers not to discuss.
Doctrinal fog is frequently used when the church changes a doctrine. The fog is often language that can be interpreted in different ways by those with different levels of belief and experience in the church. Fog allows those who like the new doctrine to see it as an improved clarification while also allowing those who like the old doctrine to still believe it because the old doctrine is rarely formally denounced.
Examples of doctrinal fog are everywhere in Mormonism when one looks at the current doctrine and compares it to what was taught 100+ years ago. An easy example is the lifting of the priesthood ban for blacks. The Church lifted the ban, but never explicitly denounced the theology that leaders once used to justify the ban. So the theology largely still continued and only started to die with the effects of silence and time. If the Church had denounced the earlier doctrine that was once used to justify the priesthood ban it would have called into question the reliability of prophets and apostles.
Repentance, admitting mistakes, and changing behavior is a foundational belief of the LDS Church and indeed of all Christianity. While this applies to individuals it should also apply to organizations, particularly one that claims to be the "only true and living church upon the face of the whole earth". However, the instances of LDS leadership admitting mistakes and errors are so few as to be almost non-existent. From a corporate perspective, it is much safer and easier to use doctrinal fog to blur past errors than it is to be honest in it's dealing with it's members and with non-members. This may be a necessity in the imperfect world we live in but in my opinion it should be used extremely sparingly and with great caution. It should not be the norm for lessons, public communications, and doctrinal pronouncements. As the church is learning through it's failing attempts to keep young people active and it's internet communications, payback can be a bitch.