There are several ways to import a web page, handled in the Import Options section of the General preferences pane. You can convert HTML to WebArchive or text. The former will retain original page presentation, the latter will convert the HTML to RTF, which does a good job of extracting the information, a reasonable job of retaining formatting, and not so good at presentation. WebArchives are immutable, and RTF conversions are, like all rich text files, editable.
It sounds like you are using the WebArchive function, which downloads (most) everything required to display the page, and packages it into a single format that is portable and works regardless of connectivity. That it looks exactly like the original web page does not mean it is loading the page from the Internet. So what you see in Scrivener after you import is an archived copy that won’t change.
There are a few exceptions to this. Apple didn’t do a 100% perfect job and some elements remain linked to the web and will change over time. This is particularly true of iframe elements, I believe, which ordinarily are nothing to worry about since most pages just use those for ads. Some pages do you iframes for actual content though, and here is where it can get to be a bother. These cases are not common though, in fact I think not all iframes are susceptible to this issue.
Snapshots wouldn’t solve the problem, because it is a problem in the webarchive format itself. If you snapshot the webarchive, even if you go back and view it later it might still change in accordance with the above bugs since the format itself is at fault.
You should be able to search within a page though. If I download the L&L homepage, and then search for “award” that page returns in the result list. Perhaps the lack of highlighting is what threw you off? [b]Cmd-F[/b]
works fine too, and that does highlight.
To say the least. 
My advice, if the information of the page is more important to you than the presentation: use the text import option. You’ll get all the benefits of snapshots and everything else that you can do with the regular editor in Scrivener, such as highlighting, annotating, etc.