SSP can be paid for a maximum of 28 weeks. Some companies choose to pay more than the rate of SSP but that is up to them. Any pay yir colleague has been receiving is in effect SSP topped up to full pay or half pay.
Once the 28 weeks SSP has been completed, Incapacity Benefit can be claimed even if Company Sick Pay continues.
If what you say is correct, they have misunderstood the SSP rules as the 28 weeks starts three days after the incapacity began and not when full pay ends.