It's not, though - when you reach the last page, the listed number of results changes to a few hundred. You can't approximate a three digit number, be off by 7 orders of magnitude, and say it's an "estimate" with any credibility.
I'm not going to say that the UX is designed well end-to-end, but Google doesn't display more than X number of results for a given search string, ever, where X is O(100). It costs way too much money and you are unlikely to find what you are looking for by showing you more than the top X results.
"I found a billion hits, but I'm only giving you two" is in no way a good defense. It is blaming the user for a completely reasonable interpretation of the language -- weasel words are not appreciated by people.
The idea that you would earnestly search through 400 records only to not find what you are looking for --but the 401st record would-- is just not a realistic use-case.
And if they want to offer your proposed crazy edge case as a service, folks needing it are willing to pay for organized information that is deep.
It's the internet. The internet is huge. I can imagine there being millions of pages that mention cows in some manner. I know google indexes the internet, therefore I would expect that if it tells me millions that there are actually millions _THAT IT CAN SHOW ME_.
When it tells me 10 million and only shows me 8 million, I'll be forgiving. Maybe exasperated, but forgiving. When it tells me 10 million and can only show 400, that exasperation quickly turns into distrust.
final short maxReferencesWeAreGoingToDisplay = 400;
final short numDisplayedReferences = Math.min(totalReferencesWeFind, maxReferencesWeAreGoingToDisplay);
I'll send you a bill for my consulting services.
I estimate my consulting charges at about 10 cents an hour. There's a help page somewhere that tells how many orders of magnitude that estimate might be off by.