No. I work for an OTA (not Kayak). First of all airlines file their fare rules and OTAs don't change the prices, and generally airlines pay around $10 to us to book a RT fare so there is little room to discount. Kayak is a meta which means all they do is present prices they are given from their partners (either via a feed or scrape) and then send them to the partner who shares the fee. Southwest (as others have mentioned) is not available in the US as a business choice. Kayak also heavily caches the fares (everyone does to make performance better) and inventory changes a lot especially in close by dates. Seeing cached prices of a cached price means the actual price can change a lot from searching to booking. Note the final price is only determined when you hit a booking page, everything before that is cached and might be fairly stale. Of course they can be errors in pricing since the fare rules are crazy complicated and often the difference in fares might be all the taxing entities. Each country, county, city, airport and cow pasture might affect the final price so it's possible that a country where you are booking might affect this (our customers are mostly in the US) but I doubt it.
Perhaps because time elapsed between when you searched and when you searched using the Incognito window? Perhaps because you hit a different load balancer with a different cache?
It's quite possible that nothing nefarious is going on.
Also note that airlines can and do choose to show more flight options on their own sites that they deny to any OTA. The actual fares are all by rule and aren't different.
I've had good luck in saving tons of money in the past when using an partner airline to book a flight as a codeshare, rather than the actual flight number.
eg, Find a flight you like on AA? Try and book it on QF or BA and the price might be substantially different, even though you end up sitting on exactly the same plane.
tldr - lucky "hacker"