This is one of the main problems with using Ancestry as a souce. The primary one is that so many of their trees contain so much incorrect information and use other incorrect Ancestry trees as sources. As has been mentioned several times in these forums, Ancestry is usually best used as hints or suggestions; as a guide for doing further research for more credible sources such as some of their data collections.
From what I've seen, these are of mainly two groups, digitized records of actual documents, and compilations of information from various sources. Those passenger. and immigration lists you mention are of the second sort. Before using the information, one has to research it's source to try to find the original source for the bit of data, which hopefully would prove to be a good primary source. Unfortunately, it has been my experience that some of the collections include "user submitted data", and when the data cannot be associated with its specific source, it makes all the information somewhat suspicious, in my opinion.
A good example is an Ancestry collection, Early American Marriages: Virginia to 1850. An ancestor of mine was listed with marriage data, but not specifically mention from where the info came. In checking out the origins of the Ancestry collection, I came across this website which explained how the collection came into being. Look at "UsageTips".
Source:Virginia, United States. Early American Marriages: Virginia to 1850
The part about user submitted information was the main clue for me. Unfortunately, I could find no other source for the information, so I had to put an alert in the profile to point out the above and to take the info with a grain of salt.
Consequently, I try to never use Ancestry as a source, unless it is of the digitized original document type and only then when I can't find the document elsewhere, such as Family Search.