Incorrect fragment digestion with non-palindromic restriction sites

Overhang's strand is not detected properly when the cut occurs on the negative strand of non-palindromic site.

From user's email:

"I've run into an issue with a non-palindromic restriction enzyme,
BsaI, when using the "Digest into Fragments" function. The cutting
pattern is below:
http://www.neb.com/nebecomm/products/productR0535.asp
When the recognition sequence GGTCTC is on the primary strand, cutting
goes correctly:
GGTCTCTAATGC
CCAGAGATTACG
becomes
GGTCTCAXXXX
CCAGAGATTAC
(where X means absent bases)

However! if the recognition sequence is not on the primary strand, e.g.
AGCGCTGAGACCCGATAT
TCGCGACTCTGGGCTATA
the cut should be
XGCGCTGAGACCCGATAT
XXXXX ACTCTGGGCTATA
(to the 3' end of the recognition sequence on the reverse
complementary strand) but the result given by the "digest into
fragments function" :
AGCGCTGAGACCCXXXXX
TCGCGACTCTGGGCTATX
(which is to the 5' end of the recognition sequence on the reverse
complementary strand.)
In other words, despite the fact that GGTCTC is on the rev. compl.
strand, it is correctly locating the sequence... and then cutting as
if it's on the primary strand. Looking at other randomly chosen
non-palindromic enzymes like BceAI, this problem does not seem to be
limited to BsaI. Anyway, this is obviously a problem if you are
trying to use the cloning functions and you are using a
non-palindromic enzyme. (I don't seem to be having this problem with
any of the palindromic enzymes I've used recently - NcoI, EcoRI,
SacII.)""