Honestly, that's quite a big question, and already includes a range of assumptions that might not be entirely accurate... such as the idea of there being "old ninja clans" in the first place...
But, to keep it relatively short, what is taught under the banner name of "Ninjutsu" today is actually a collection of different (but related in a number of cases) martial and ninjutsu systems which have a variety of histories (in many cases embellished at the very least). Some of these systems (Takagi Yoshin Ryu, Kukishinden Ryu, and likely Shinden Fudo Ryu) are verified and known outside of the "Ninjutsu" schools, either as alternate lines, or related arts (and, if dealing with the Genbukan, the list of otherwise recognized systems grows, including Asayama Ichiden Ryu, Daito Ryu, Bokuden Ryu, and a few more). The more "ninja" systems (Togakure Ryu, Gyokko Ryu, Koto Ryu etc) are more problematic in terms of historical verification, due to the aforementioned embellishment, combined with gaps and, well, errors in given history. There's a fair bit of circumstantial evidence that supports the systems, the methods largely fit what would be expected, and so on.
From there, a number within the Bujinkan have claimed to see particular evidence... but never give details. Not really sure why not, myself...
Oh, and for the record, what's taught in the Bujinkan today (Budo Taijutsu) may be sourced from the systems... but it really isn't the same thing. What you see in most Bujinkan schools (that I've encountered) is really what is in the Ryu (systems) themselves, on a range of levels....
