This belief seemed to spread in April 2011 via twitter.
Due to Ryanair's reputation as being overly greedy at the cost of the consumer, I think many people have simply assumed that this claim was true.
It does not appear that it has been looked into too conclusively, but the investigations that have been done indicate that the claim is not true.
Popular travel blog tnooz investigated this, which has an unsourced quote from a Ryanair official denouncing the claim as untrue. tnooz refers to a company called Invisible Hand which make a browser addon of the same name which helps to find the lowest flights on airline websites.
Invisble Hand tested this claim by running 52 flight searches in Firefox and Chrome over 2 days, with cookies being consistently cleaned from Chrome but not from Firefox. The conclusion they reached was:
“If the price manipulation allegations were true, we would have
expected to see price discrepancies in the results between Firefox and
Chrome on day two. What we actually saw were exactly the same prices
on both browsers.”
It isn't a comprehensive test and doesn't take into account the possibility of manipulation based only on certain usage patterns, but is interesting nevertheless.
Given the widespread attention this news item received, if it were the case it would seem reasonable that it would have been independently confirmed. However there were no reliable reports of reproducing what was reported, which along with the Invisible Hand results may indicate that some sort of bug was encountered rather than a deliberate action.