Utopia is no place. Reality is limited. Choose wisely.
Integrity can be "compromised", be it physical integrity (the structural support of the building was compromised and so it collapsed) or moral integrity (their values were compromised and they did a bad thing).
But compromise can also be a concession in pursuit of a value. My wife and I want to go see a movie. I want to see a horror and she wants to see a romcom. So we compromise and see something that was not a first choice for either of us but that we're both happy with since the superior value being sought was spending time together. The specific movie was a secondary value.
In this second context case I disagree that compromise CREATES value, but after I read the blog I realized that the author didn't even mean what the title literally says. The author is saying that it is difficult for someone to have NO values (in a literal sense this would have to be a very depressed individual who is contemplating suicide since they do not even value their own life). But that some people move through life mindlessly and aimlessly, oblivious to what they value. So much so that they do not consciously value anything. And so once such an individual is "forced" to make compromises then the recognition of values is then forced. I suppose the author's thesis is that forcing a recognition of values could lead to the adoption of values previously unconsidered.
I think generally we have the same values. Honesty, transparency, integrity, expediency, travel, etc. However what we don't share is priority of them. To the author's point, do you value having pets more than you value freedom to travel? Reasonable people could disagree. And there is compromise to be had, but if you're not careful you can get the worst of both worlds by trying to split the difference.