Referencing references that reference references? How deep do you need to check for "accuracy"?
While the system isn't perfect, the purpose of the reviews done by publishers prior to publication is to assure readers that what is said in a paper can be trusted. Some reviews take a long time and some papers require several iterations to reach this point.
So, in general, you should be able to trust what you read in reputable journals. Other journals, not so much.
But, mistakes happen and sometimes group think can interfere. If you have a reason to doubt something, then investigate it further. Perhaps that is by following references, and perhaps it is by looking at orthogonal sources. But the judgement is yours to make.
For a student, getting in to the game, however, the judgement can be in favor of deeper study rather than trust. If you don't understand something in a paper it is probably a bad idea to quote it in another. If you misunderstand something, you may also misunderstand its implications. So you look deeper until you begin to get the insight(s) that the chain of authors had earlier developed.
Trust, but verify.