The fact under contention is very specific, not just general vaccine hesitancy. The article appears to fail to mention it, unless there is some other quote that can be shared beyond the paywall. More interestingly, here's an approximate heatchart of the probability that a given paragraph in an article will be read by the average reader, by the position in the article the paragraph appears:

  ****************************
  *****************
  *********
  ****
  *
  *
  .
  .
  **

There is a huge difference in attention between (free) headline & subtitle, and a (paywalled) paragraph squirreled somewhere near the end, which I am willing to bet is the case for the nyt article.