It depends on how you define "grown up speaking". That sounds pedantic, but a bunch of recent scholarship, specifically articles by Christopher Baswell, Christopher Cannon, Jocelyn Wogan-Browne, and Kathryn Kerby-Fulton in vol. 90 no. 3 of Speculum, one of the major journals for medieval studies, has challenged the basic idea of "vernacular" language and the notions of "birth tongue" that goes along with it. The aforementioned scholars argue that a vernacular is situationally dependent. For many clerics, Latin may have indeed been the language in which they thought, even if it wasn't the language they spoke, and a similar argument can be made for French in the English royal court at certain times.

So, Kramer may have first learned one of the French or German dialects of the region, but, given his induction into the Dominican order at an early age, it may indeed be fair to say he grew up speaking Latin. He certainly shows a great proficiency in it. But I know of no systematic argument one way or another. If you read the above articles, it may quickly become clear that this is the sort of question that usually only bothers Insular historians.