Firstly, let’s clarify the “line” – only the original tiles on common areas are Common Property and therefore the responsibility of the Owners Corporation; that’s the floor, any walls that adjoin other Lots, and any walls that also the outside walls of the Building.
Secondly, any replacement of those original tiles by Owners must receive the Owners Corporation’s written consent in advance of the works being undertaken, and it is usual for any written consent to include a statement to the effect that all future works to maintain, repair, and replace those replacement tiles is the responsibility of the Lot Owner (the current one, and all subsequent Owners).
With regard to your Executive Committee Members’ proposal to introduce a special levy for their own benefit, that would be in conflict with the Developer’s obligations under the Defects Warranty, would also deny them their legal right to be given the first opportunity to undertake corrective works, and likely void their responsibility for any other related works in future. Furthermore, that special levy would require the agreement of a majority of Owners at a General Meeting; surely you could muster enough support to knock that on the head!