There was widespread international correspondence, of course it was not as easy as today. Some Reformers wanting to find out the state of doctrine in the East is not surprising, and many problems they had with Rome were then also found in Constantinople (justification, predestination and so on). For theological reasons there was no union between Protestants and Constantinople and the political situation was that Constantinople was already Istanbul.Indeed I'm approaching this from a scholarly angle. For what it's worth, correspondence today is no big deal, but in the 16th century it was quite a big deal since no established mail routes existed. Writing and sending letters then was expensive and fraught with getting lost. I would caution couching modern expectation against those of the past.
Consequently, the book of Concord was published in 1580, well past Phil's and Marty's life and more as a response from the emperor's desire to calm the tensions created by unanswered religious questions. So much at that time was in flux and wasn't "solidified" until 1580s.
It's tough separating what is political versus religious since it was so intertwined in those days.
Regardless, I'm going to seek out the book I mentioned above.