"We have conducted a review of our files and have been unable to identify any Food and Drug Administration (FDA) records reflecting the approval, clearance, or listing of these devices."
They were seeking to fly under the radar as a "lab-derived test" or LDT, using an FDA loophole that the FDA is increasingly seeking to close (also see Theranos). The "we've reviewed the literature" part is just the FDA's attempt to dig into what's been published to see if they can find ANY support for their marketing claims — even if there were volumes of papers on their method, they still would have been sent the warning letter (which is a Very Serious thing to get from the FDA).
The issue wasn't that "this test is too risky for us" it's that they were 100% out of compliance. If you sell a medical device, it must be classified for risk and at the very least registered with the FDA. In the case of a cancer diagnostic, there is zero chance it would be a Class I (lowest) device, so they (at least) would have needed "clearance" requiring a submission of something called a 510(k) documenting tests they've done on their product, audits of suppliers, etc. etc. In addition to the 510(k) submission itself, they would need documented evidence of having put in place a "quality management system" that puts standard operating procedures around 100% of product development from cradle to grave. This is why health tech/biotech companies need to raise so much money, as this is a lot of overhead.
If their test were classified as Class III (highest risk), they would need "approval" rather than "clearance," the bar for which is even higher (although this is primarily limited to ingestibles/implantables). Just the FDA submission itself costs something like a quarter million dollars.
GRAIL, on the other hand, is raising a huge amount of money partially because they know how much it costs to run proper trials and earn a clearance or approval. It's apples and oranges to compare the two.