But only if they actually read the claim. This is the same as for scholars that cite the source of a claim they found in a paper that is, itself, cited from some other paper. Often you see a game of telephone in these citations. Because it's not looked at well to give a factual claim you found in a review paper, researchers often cite the claim as it was cited in the review paper, but they don't always investigate the claim themselves. This leads to a game of telephone.
A lot of high-profile factoids are like this. The claim that 95% of diets fail, for example, is a specious one that developed after a citation chain like this. The original analysis said that 95% of the sample finished the study above the lowest weight they reached. Through motivated rephrasing and citation laundering, this became 95% of diets fail, often paired with the suggestion that dieters always return to a weight higher than where they started.
Yet, you can find this claim being re-issued again and again in the introductions to papers about all sorts of topics related to dieting.
Another thing I have seen is where the source of the claim gets lost. It starts out as something like "Grainger 2003" and then eventually turns into "Grander 2013", a nonexistent paper with a ton of citations.
So, if you read an article and don't read the cited article, please reference only the article you read.