In theory you are right, but in practice not so easy. The fitting in the carpet has a round 'turret' of 17mm dia - on top of which is located a round swivel, also 17mm dia but shaped as an oblong. I would think that the original mats that used these fittings had a 17mm hole on top of which must have sat a washer with an oblong cut out 17mm long to fit the swivel, which, when turned 90 degrees retained the washer and mat in position.
The other problem is that the turret is only 5mm between base and swivel, the new mats are 6mm thick without any washer to put under the swivel. Also the obvious mounting points do not line up with the turrets.