I just tried "private tab" with iPad Safari. I did not get that message, but on the bottom saw "using IP location".
I guess it could be considered an invasion of privacy, if there is such a thing as privacy these days. It could also be considered a service.
For example, if I lived in New York and wanted to find a local basmati supplier, I wouldn't be interested in retailers located in San Francisco or Miami, but Newark would be OK
Because you are concerned about this message in relation to SEO, this is something you may actually want. If you are interested in getting a very rough idea of how the results might be positioned for a "world set" of results as opposed to a "local set" of results, not letting Google know your location might make a difference. Of course if Google knows your search history any result positions will likely be skewed based on your past known preferences.
IMHO, doing searches with the assumption that other searchers will see the same positioning is a faulty assumption. The good news is that after ensuring that a page can be found you can focus attention on more important things like making site improvements that increase conversion.