While you can make a case his views on collective bargaining and government employee unions were only related to federal employees, you cannot make a case that the library, its website and the documents contained within show my bullet points to be inaccurate. The letter you refer to is in the material from the library. You had stated in a previous post that he was for collective bargaining. There is absolutely no evidence to show this. I know it is difficult, but the words you are looking for are "I was wrong".
This line from that website pretty much shoots down your claims that he was opposed to public employees being able to collectively bargain:
One can't say he was opposed to public employee collective bargaining because there are no references to him supporting it. I would submit that in his years as president he never pushed to ban or not allow that ability. Had he done so, I would agree with you, but he did not. I posted an excerpt from a letter he wrote that states he was indeed opposed to strikes by public employees. He referred to them as "militant" actions. So really, your bullet points are not accurate given the excerpt I cited from the page you posted.