Yes, indeed, that is very true and I run across this problem every week in my mechanic work.

The way has to do with load. A starter may only draw 60A on the test bench (out of the car). At load (when turning an engine) it may draw up to 300A. Partially clean connections are not good enough at these high amperages.

Connectivity test does not matter when the starter asks for 300A - unless the connections are Very Clean.

Pretty clean means not the same thing as "cleaned down to shiny bare metal". See Battery Mainenance for instructions and photos.