Lounge access is always subject to local restrictions. Particularly at outstations, where capacity is often limited, many airline lounges restrict access to passengers travelling on that particular airline only.

Of course, in many places you are free to lounge-hop to your heart's content, but this is never explicitly guaranteed by any alliance. As long as you have a business class (or higher) ticket, or an economy class ticket but hold the relevant Skyteam status, there should be at least one lounge available to you in most locations. If another Skyteam lounge denies you entry, then they should be able to direct you to the *correct* lounge for your particular circumstances - as appears to have happened in this case.