They are known to be the richest club in the EPL, so I don't know why they are pleading for Manchester City to support them by accommodating their players in the flight.
Ratcliffe's have done many things in the recent past as cost-cutting measures and probably they didn't want to pay for a private jet just for two players but it's some insane level to take the cost-cutting.
Many sources reported that the incident is true.
For a private jet it might be too expensive but there are other planes available, if they both take a commercial plane I don't think it will reduce the credibility of a club, if it is indeed a savings, but if they fail to go it means being stingy and not wanting to lose out