FDR and unions

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There has been a number of things recently suggesting that "even FDR was opposed to public employee unions." An example is the following from the Monmouth Musings.
Even President Franklin Roosevelt, a friend of private-sector unionism, drew a line when it came to government workers: “Meticulous attention,” the president insisted in 1937, “should be paid to the special relations and obligations of public servants to the public itself and to the Government….The process of collective bargaining, as usually understood, cannot be transplanted into the public service.” The reason? F.D.R. believed that “[a] strike of public employees manifests nothing less than an intent on their part to obstruct the operations of government until their demands are satisfied. Such action looking toward the paralysis of government by those who have sworn to support it is unthinkable and intolerable.” Roosevelt was hardly alone in holding these views, even among the champions of organized labor. Indeed, the first president of the AFL-CIO, George Meany, believed it was “impossible to bargain collectively with the government.”

However: In Anchor Rising you find the following:
In a letter to a public employee union, Roosevelt explains that, yes, they do have a right to organize, but there are some restrictions:

"All Government employees should realize that the process of collective bargaining, as usually understood, cannot be transplanted into the public service. It has its distinct and insurmountable limitations when applied to public personnel management. The very nature and purposes of Government make it impossible for administrative officials to represent fully or to bind the employer in mutual discussions with Government employee organizations. The employer is the whole people, who speak by means of laws enacted by their representatives in Congress. Accordingly, administrative officials and employees alike are governed and guided, and in many instances restricted, by laws which establish policies, procedures, or rules in personnel matters."

"Particularly, I want to emphasize my conviction that militant tactics have no place in the functions of any organization of Government employees. Upon employees in the Federal service rests the obligation to serve the whole people, whose interests and welfare require orderliness and continuity in the conduct of Government activities. This obligation is paramount. Since their own services have to do with the functioning of the Government, a strike of public employees manifests nothing less than an intent on their part to prevent or obstruct the operations of Government until their demands are satisfied. Such action, looking toward the paralysis of Government by those who have sworn to support it, is unthinkable and intolerable. It is, therefore, with a feeling of gratification that I have noted in the constitution of the National Federation of Federal Employees the provision that "under no circumstances shall this Federation engage in or support strikes against the United States Government."

So perhaps it was just public employee union strikes that FDR opposed not the existence of the union itself.