Why do people with Down syndrome get fewer cancers?
This is a great question. Just to make it clear people with DS do have a reduced risk of solid cancers and an increased risk of blood cancers, (B-ALL and AML).

You are correct in picking out DSRC1 because of its angiogenic implications. The current hypothesis centers around people with DS being less capable of driving angiogenesis, and therefore having an internal environment that is less nurturing to metastasized or even developing solid cancers. Current unpublished work I have recently seen shows this very clearly in the eye, where the vasculature in DS is far less branched than in the wild-type population.

Why however they show an increased risk of leukemias is a largely unanswered question, with one exception being AMKL (Acute Megakaryocytic Leukemia). People with DS are at a ~500X increased risk of AMKL over the unafected population, and it appears to be entirely driven by the in-utero introduction of a stop mutation in codon 2 the transcription factor GATA1. This transcription factor is important in driving differentiation of progenitor cells in the bone marrow to become erythrocytes and megakaryocytes. Thus inactivating this transcription factor plays a large role in disrupting normal hematopoiesis such that megakaryocytes are overproduced and become a leukemia.

All that being said, and as you mentioned people with DS have around a 20-50X increased risk of AML and B-ALL. There are certainly some chromosome 21 genes that have been implicated in this like Bach1 (important in DNA repair) Ifngr2 (plays a role in cell death) Usp16 (epigenetic regulator Really important recent Nature Paper) and Runx1 (important in stress response) but the field is entirely unsure why this directly leads to increased risk of leukemias. Many current cancer biologists favor the direct gene-dosage problem that people with DS face in that a some ~120 genes are overexpressed when they shouldn't be, and assume that these gene level cocktail directly leads to this increased risk of leukemogenesis, and this very well may be in part the answer. There is however a great 'contrarian' view, in that hematopoietic stem and progenitor cells will become pro-apoptotic and pro-differentiative when faced with certain stresses like aneuploidy. The effect of this on a global scale would be that many of the stem and progenitor cells in the bone marrow would die or differentiate prematurely. This would then result in teenagers with DS having far fewer blood stem cells then they should, and these cells would then be tasked with pumping out more blood per cell than originally meant for them quite possibly leading to an exhaustive phenotype. In this way the blood systems of people with DS will 'prematurely age', and might thus rapidly increase the risk of cancer.

Make sense?