This has been my explanation, which is routed in fact, but can be misinterpreted as 'the nasty airlines squeezing money out of us'.
Basically, online booking engines for traditional airlines sit on top of GDS's (1970's technology that works fine).
When you search for say 2 seats from LHR-FAO and get quoted 2 seats at BA's cheapest O class fare (say £50 o/w) it removes them from the general inventory for a period of time (about 5 minutes) which allows you to finish the booking / PNR (add your names and contact details basically). After 5 minutes these confirmed O Class seats (HK) if they havn't been confirmed booked revert to NN (Need Need we call) and the 2 seats get returned to general inventory.
That's fine if there are 9 O class seats available. But what if there is only 3?
You've removed it from the inventory. If you got distracted, and go back and search again then you've removed 2 which are in what is euphemistically called 'the black hole' and get quoted instead 2 x Q class seats (at, say £70).
So it looks to the layman that BA has spotted your interest, and increased the prices. But in reality it's your own fault

But if you wait 5 minutes for it to return to the general inventory then you run the risk of someone else having booked it up!
This may happen rarely, but with the amount of enquiries / bookings if it happened 1 in 30 or 1 in 50 times (could be less) then that's enough for people to think there is dynamic browsing / thievery about.
So it short it doesn't happen for airlines who base their technology on GDS's, but who knows for the airlines who don't (Ryanair, Easyjet etc)? I'd also suspect not.
Sorry for the ramble