That's not what Bing AI is doing, at least not yet. Bing AI doesn't make any HTTP requests to external sites, even with prompting. And if you think it does, I'd like you to produce a server log showing that's the case which should be very easy to produce.
My understanding is that the Bing AI is reading whatever the Bing crawler has already cached.
Or even simpler: "Sidney" is able to retrieve contents from URLs because the contents are part of whatever dataset was used to train it, and the URL may be part of the dataset. This too shoul be easy to test by asking facts about webpages both before and after the datasets' cut point.
My understanding is that the Bing AI is reading whatever the Bing crawler has already cached.