The view one takes on the credibility of the assertion is going to depend largely on one's presuppositions and level of allowance for the Bible text to speak for itself.
If the Torah (Law, i.e. "teaching" is the idea in Hebrew, not just the actual commands and prohibitions), which includes Genesis, was formed contra what critical scholars claim, and instead ...
- was in fact essentially singly authored by Moses (with possibly a few final editorial editions by Joshua [about Moses's death? Dt 34:5-8], who is recorded to have added further information to the Law in his own time in Josh 24:26, though that only sets a precedent for his additions, as the passage itself is more specific to the renewed covenant vows of the people in v.19-23), and
- was largely "dictated to Moses by God" (quoted from above link on Mosaic authorship), some being written both before ever ascending to Sinai (Ex 24:4), some upon Sinai (actually stated there to be given by God initially; Ex 24:12), and most likely after the fact during the tabernacle meetings with God (of which Joshua was also privy to; Ex 33:7-11), and
- was essentially complete at the time of his death, and entrusted to the priests for reading to the congregation every seven years (Dt 31:9-13; whether this was ever practiced or not in its entirety is questionable—later tradition only read "selections from the Torah."), ...
then there is no credibility to the assertion at all (disclaimer: this is my view). This indicates that the history contained in Genesis, Scripture declares God revealed to Moses. Such an account from "the God of truth" (Isa 65:16), the One who is and does right (Gen 18:25, Ps 7:9, 11:7), and was there (Gen 1:1), is then the true account of creation, which being mankind's history, those events did become a basis for the various morphed forms of that history by various cultures across the planet (including Sumerians).
Of course, if one rejects points 1-3 above (in line with critical scholars), and rather favors more direct pagan influence on the Hebrew scriptures, then there is at least plausible credibility for the assertion that the Sumerian works influenced the Hebrew works. There is of course some pagan influence, as the Bible addresses aspects of paganism both in the nations around Israel and within Israel itself, but that is a different category of influence than what is asserted with the early chapters of Genesis—the former idea condemns the paganism, whereas the latter would attribute pagan ideas as an "imprint on the Hebrews" (per your quote), rather than looking further back to the history itself that imprinted them both.
So presuppositions drive how one reads the evidence, and thus will lead to differing views on the credibility (and nature of) the relationship between the two.