As others have said Chris, it could be a number of things, but it does sound like it wasn't quite set up right.
Tyre pressures make a huge difference on all bikes and so does the amount tyre wear but since you were on a test ride, there wasn't much you could do about that. I remember riding a GSX-R 750 on a test ride once and it just would not turn for love nor money, but as soon as my mate got new tyres on it, it was a different bike.
Others have mentioned rear suspension and jack up kits, and all I can say is that having done both to mine, it is incredibly quick steering compared to what it was, and my ZZR1400 in particular. Now there's a bike that really needs muscle to turn at high speed. The trade off for me running it so high at the back is that it is unstable past 150, but unless I'm on an Autobahn, I'm not too bothered.
You said you wanted a bike to grow into and the FZS is that bike. It's very cheap to run compared to many other bikes, and very cheap to modify. For example, Ivanising the carburettors for a smoother (and quicker!) ride is 120 quid, Devilsyam of this forum sells R6 rear shock kits for a hundred or so. Things like discs and rear suspension linkages will go 100,000 miles easily, and of course, there's a huge amount of info and help waiting for you on this forum.
I'm biased though. I've ridden a lot of bikes and after 10 years of ownership, I reckon the FZS is one of the best ownership propositions ever, from cost to riding pleasure to reliability to comfort. And it's still a bloody quick bike even 12 years after it's launch.