Providing the information on a publicly accessible page provides permission. It's like posting a letter on a public noticeboard and demanding that certain people not read it.
There is a distinction between a person reading one page and a scraper reading all pages.
First, the scraper consumes a lot more bandwidth (which some websites might have real trouble with). Second, the aggregated scraped data is a lot more valuable than what any single person receives from reading a few pages.
Websites could (and sometimes do) limit the number of views and the frequency of accesses from the same IP, which allows users to read the page and discourages scrapers without "taking it down".
not so much "demanding that certain people not read it" but demanding that certain people not take certain action with the information on the notice board.
If you don't want it read, take it down.