British Airways - Denied to onboatd at Hyderabad Airport

Hi,
I stay at Netherlands and where as my family (Spouse and Daughter) stay at India.
Since I was missing them a lot and wanted to celebrate my Baby birthday (**th Dec’**) at Netherlands, I have made for them Visiting Visa (under Visiting Family/Friends – Visa type - C).
I booked a ticket for them through makemytrip.com to travel From Hyderabad-London-Amsterdam on **th Dec’** and return on **st Jan’** same route.
Below are the details:
Booking ID: Booking Id: IN*B*************
PNR: LWRWPW
But when reached to Hyderabad Airport British airways representatives stopped them to onboard the flight as they do not have the transit Visa.
But before I book the ticket in British airways via make my trip nowhere else it is mentioned that we need a Transit Visa.
And when I trid to book the tickets via britishairways.com to verify whether we have any note or pop-up asking for the Transit visa but no wher else it mentioned even we went till the payment mode.
and when I verified the Transit visa rules they mentioned the below
Transiting without a visa
You might be eligible for ‘transit without visa’ if:
• you arrive and depart by air
• have a confirmed onward flight that leaves on the day you arrive or before midnight on the day after you arrive

Based on the above condition, they both are landing in Heathrow Airport in terminal * and there is a layover period of * Hr ** min and taking the other flight to Amsterdam on the same day and from the terminal * only.

So how the people will stop at Airport? Now they have missed the flight and I really disappointed.

Please check this scenario and respond me asap with explaanation
And to be very clear none of the passengers will know about these conditions unless you mention in the site before we book the ticket.

Please help me in this regard and I need to get my refund.

Please reach out to me +*********** for more details.