I think what you are thinking is consistent with what I said. Best to illustrate with an example:
Let's assume that the sequenced locus is actually C/T. What we likely hopefully see assuming a read depth of 20 at that position, is approximatley 10 C reads and 10 T reads (correct me if I'm wrong). If the human reference is TT at that locus, then if everything goes will the caller should call CT, right?
In the 2nd example, let's assume that a single strand library is prepared (which is often the case with say ancient DNA that is degraded and has less than 5% endogenous material). In this case things get a little tricky I would think, because let's assume the actual SNP sequenced is a C and the read depth is 3, and we get 2 C reads and one T read. If the variant caller comes back with a CT because the reference is CT at that locus, we may have a problem. Is there a way to tell the variant caller that the actual sequenced material was single strand, and for it to return only 1 allele?