Many people feel uncomfortable when others say, "I know . . ."
I think the confusion is strongest among those who feel that it is impossible to KNOW anything - that it is lying to say, "I know . . ." The issue to me is how we define "know" in the Gospel context - and how that relates directly how we view bearing a testimony.
Nephi said that he "knew" because of what he had "experienced". (My paraphrase)
I have had numerous experiences that really are impossible to explain without God being real and the Priesthood providing abnormal insight. I mean that, knowing full well the arguments of the skeptics. If I shared the details, it would be possible to reject them, but it would be impossible to say that my conclusion is not valid, logical, reasonable and possible.
When Elder Packer spoke of testimonies being strengthened by the sharing of them, I believe he was saying that we need to express those things that we believe with all our hearts - that we believe to be true "of ourselves". I also never read anything in the talk that said we need to exaggerate or couch things in specific ways. I don't read in his words the commonly expressed, "Fake it until you make it." In my opinion, that is a twisted translation of the meaning he was trying to convey - and I absolutely hate that expression.
Bearing a testimony can be as simple as saying, "I believe with all my heart" - and it is that type of statement that can bring surety through spiritual confirmation. It can be no more than the willingness to open your mouth and experience it being filled - being willing to let the Lord speak through you without anything being planned in advance, and then realizing what you said was inspired and exactly what the other person needed to hear.
I have had that experience, as well, and it is moving in a way that is hard to describe.