Basically, you are implying that the algo is programmed as...
if Keyw = popular then
.....rank according to backlinks
if Keyw <> popular then
.....rank according to on-page factor/s
Isn't that in contradiction to Google's statements?
How does Google rank pages? The basics [google.com]
PageRank Explained [google.com]
Secondly, either you are implying that Google have 2 set of algo or the algo itself is selective. Of course it's not possible to have 2 algo running and if the algo is selective then it is no longer an algorithm. Algorithms are designed to cover all possible situations or events with minimum or without manual adjustment which means the program cannot apply one condition to one site and a different condition to another site. All conditions are applied accross all sites, that's the only way to determine the accuracy of the algo and not 'tend to'...
Google state that...ranking is based on the combination of 100 factors and PR(algo), using sophisticated text-matching techniques and examine all aspect of the page's content...
The above statement, is Google own declaration of what 'each' site has to go through in order to be rank accordingly. If we have to believe this then we have to believe that 'indeed' each site content is being examined and has to go through 100 factors.
How do you explain then the parked domains and pages that have moved to a different domain? When the most important thing...content...is not even there.
The easiest way to prove a hypothesis or a statement is to disprove it. If you could not disprove a statement then the statement is true. However, even if just a single event contradict the statement no matter how small is enough to disprove a hypothesis or a statement.
In the case of Google ranking algorithm, surely what they claim what they are doing does not match what's showing in the serp. Most blatant of that is the case of a parked domain(inactive) that still rank on it's old keyword months after months. Where is the part of the Google statement 'examines all aspects of the page's content ' was applied on this case? The same case with 'The site have moved' pages.