On closer inspection of your question, I am revising my answer. What you're trying to convey is "Does this company have a failure (i.e. non-compliance to some standard)? Yes or No". In which case, color is irrelevant, it's not a failure, and a check mark is somewhat standard.
Consider a table where multiple types of the same thing, like a tablet computer, are being compared. The tablets are listed on the left side with the features they do or don't have listed along the top.
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Checks are used to indicate the presence of the feature. In your case, the checks indicate whether the company is in violation of something or has an alert. Now, I think the confusion comes in because you have an alert icon for the "Overall Alert" column. If you had check marks for both columns, it would be more clear that you're conveying a "has this, doesn't have this" relationship instead of "alert! pay attention! failure! do some action!". If, however, you do want to encourage the user to act based on the data, then my original answer holds:
Using a red checkmark would not translate for users with red-green colorblindness, as well as some other types of colorblindness. Checkmarks generally represent success and shouldn't be used when you're trying to convey a failure situation. The "X" is generally understood to mean failure (see form validation and other errors all over the web).
However, made clear by our answers and @Marjan Venema's comments, the column title is misleading in conjunction with either a check or X. An alert icon, or better yet, an icon plus text saying something like "X has failed" would be more correct.