There were issues earlier this year regarding something similar where DL would show a higher price to elites if they were logged in. Supposedly fixed, but with the recent changes to the website I don't trust anything there and I certainly wouldn't put it past them.

I know that searching for award travel can jack up the price due to the perceived 'demand' by the booking system, but that is not cookie dependent.

Its also possible that you saw prices fluctuate as DL was messing with their inventory buckets or loading new fares.