A few facts to throw into the mix.
The aircraft was a B757-200, and all of TUI Airways' fleet are a Y221 configuration. The 'last-minute aircraft change' quoted was irrelevant in many ways.
This particular aircraft had the row of seats temporarily missing due to a defect, and anyone with any knowledge of AOG spares will be aware that a row of seats for a B757 are not easy to come by these days - they simply aren't available on a shelf, and not quick to produce.
Where 221 pax were booked onto previous and following flights, they were refused at check-in (due to the operator hoping for noshows to avoid a denied boarding situation) and offered alternative flights home with ground transport where required. Unfortunately, on this occasion, this was missed.
Despite the crew seats in the galley not being available, there are crew jump seats in the centre of the aircraft on a B757. The parents could have easily sat here for the duration of the flight if they wanted to, there was no-one forcing them to sit on the floor. But that doesn't look quite as good on TV, does it?