The nut slot height only causes buzzing on open strings; once you fret, it's removed from the equation. UNLESS its buzzing behind the fretted note which happens sometimes.
Yes you need more relief if the string check shows no space. Don't worry about the factory settings, set it up to suit your tastes. The length of a bass neck makes it very sensitive to climate changes throughout the year ( or travel) and requires tweaking, especially with low action. Read all you can about setups.
'73-4 Ampeg V4B, Ampeg PF350,PF115HE, PF115LF, 115 Traynor, 1962 Fender Jazz, 75 Gibson G3, '10 Squier VM Jazz, Squier CV 60's P Sonic, Squier CV 50's P blonde, Epiphone Thunderbird IV