So when researchers talking about their sequencing projects, some of them are taking blood samples from cancer patients who don't have blood cancer.

I understand that because blood cells are not cancerous, they would not show somatic mutations associated with the tumor. 
But this does not necessarily mean that they don't mutate at all right? To know if a mutation was germline or somatic, you would need the parents to be blood sequenced as well right? So my question is how can you be confident that a new variant from a blood sample in a child that has some disease (which the parents don't have), is a novel germ-line mutation or a somatic variant (without sequencing parents)?

Some researchers were arguing that rare diseases only arise from de-novo germline mutations, but I don't know how you can tell.
There are a couple of things to unpack here, most of which really focuses on the biology of what is going on versus bioinformatics. I spent my Post-Doc working on genomics projects in rare Mendelian Disorders where the gene mutation was not yet known, and while I continue to do that as part of my research my day-to-day job is doing clinical NGS in cancer. So I've done both sides of this.

The main thing to keep in mind is that somatic mutations occur originally in a single cell. In the context of cancer, this then arises into a tumour through the proliferation of those cells, some of which will go on to acquire their own mutations. So when we sample a solid tumour we typically get a mix of tumour cells and normal cells, so when we do the sequencing the detected allele frequency of a given mutation, and thus the proportion of reads with that mutation, is at most equal to the fraction of tumour cells in the sample. There is a caveat to that last statement because of course, many cancer cells are also polyploid, but in general, it's useful to consider the previous statement to be true most of the time. Somatic variant callers are tuned to detect variants at a range of allele frequencies. Emergent mutations related to treatment resistance for instance or subclonal mutations may be well below 1% of the reads in your sample.

The programs we use to call germline variants are entirely different from those that call somatic variants and are tuned to identify and genotype variants that appear in allele frequencies consistent with homo or heterozygosity. 

So when we draw a blood sample from someone without a blood cancer or other proliferative disorder, the fraction of cells in that sample with a somatic mutation will be quite small, and it will be very inconsistent between cells. These will be below the thresholds to trigger variant calling and genotyping by germline variant callers in general.

De novo mutations are mutations that arise in the sperm, egg, or sperm-producing cells of one of the parents. They are not typically a somatic mutation in the child, although technically a mutation that occurs at fertilization before the first cell division would also be a mutation in100% of the child's cells, and some rare diseases are due to mosaicism but the first is pretty rare/unlikely to occur in the scheme of mutations per generation and the second is kind of a deviation away from the norm that might not really even be considered a Mendelian disorder depending on who you are talking to.

So, we do not need to sequence parents to distinguish germline from somatic variants in an individual. We do need to sequence parents to properly identify de novo mutations. And rare diseases only arise from de novo mutations in the sense that all mutations, at some point in their history, are de novo mutations. But after that point, depending on the severity of the mutation, they can be passed through generations. Rarity is a matter of frequency of occurrence, which many many factors contribute to.