Often not, and for lots of different reasons.
Citations about related work, background information etc. are often given to give the reader the context of your work, but your work does not necessarily depend on the results therein.
Seminal results from decades ago are sometimes in German, French or Russian, and while I might occasionally struggle through papers in the first two languages if I desperately need to see how something was proved, I will usually take the results on trust, especially if they are heavily cited.
And then, some results are just too complicated, but are sufficiently well accepted that there is really no choice but to rely on them - most group theorists will use the Classification of Finite Simple Groups when necessary, but few, if any, will understand the full details of the entire proof. On similar lines, I cannot possibly read the Robertson-Seymour series of papers on Graph Minors. Yet I believe the main results in them, and if and when I refer to the fact that any minor-closed class of graphs has a finite set of excluded minors, then it is pretty much obligatory to refer to the relevant paper in the series.
If correctness is seriously in doubt, then it would presumably be necessary to work back not just to the papers you cite, but to the papers they cite, and so on.