In German, unvoiced consonants are frequently, if not always aspirated, and the aspirated and non-aspirated consonants are allophones which do not make a difference in meaning.
In fact, spakers of German often find it hard to even tell a difference between aspirated and non-aspirated unvoiced consonants; and similarly, speakers of German who are not used to languages which do NOT aspirate their consonsants (or in wich aspiration makes a difference in meaning) also tend to perceive a completely unapsirated unvoiced consonant as voiced, e.g. /p/ would be perceived as /b/ when pronounced without any aspiration.
So the tendency goes towards the unaspirated unvoiced consonants diverging into the more distinct counterparts, i.e. /b/ and /ph/ in the case of /p/, and one might claim that a pure, fully unaspirated unvoiced consonant does not even actually exist in German, but I don't know about any phonetics studies that would confirm that the /p/ is definitely always aspirated, probably the pure /p/ without any aspirations still exists.
So, I'm not sure one could claim that German does not have unaspirated consonants at all, but at least it is a language in which /p/ and /ph/ are not disgintuished in the sense that they can be used completely interchangeably or /ph/ is not even perceived as something other than /p/.