An interesting data point on this.

Both my partner and I got these texts at eactly the same time last week, two days after a cancelled flight home from Nice. We were on separate bookings as I was on business and he came along on Avios.

However, I made his booking using the family account and I used my phone number on his booking. When the flight was cancelled I got texts from BA for both bookings, he got the email but not the text.

But the text from Skyclaim for his ticket came to his phone number not mine. His number is in his BA account so unless BA systems send both the booking telephone number and the executive club phone number to ground agents etc it seems likely the data breach is on BA's side...