If other shops in the past have replaced batteries there and then with no problems then I'd suspect yes, the Timpsons bloke is trying it on and what he's got in mind is; take your watch, charge you for sending it away and recalibration, when the reality is he'll change the batteries and keep it in the shop for a week
If it's possible, see what another shop says (just ask for the battery to be changed, don't mention calibration or anything the Timpsons bloke said - it might give 'em ideas).
Cynical? Moi? Never