Hi,
I have a question about interline agreements.

I'm flying from Glasgow to Auckland via Heathrow and Taipei on a single ticket with same PNR booked through China Airlines.

GLA to LHR is with BA then the next 2 legs are with China Airlines.
BA and China Airlines have an Inter Airline Through Check-in agreement (detailed on China Airlines website) which I presume means that I can check-in in Glasgow and my baggage will be checked through to Auckland and I will also get all 3 boarding passes in Glasgow.
That's the info that I have got from everywhere I've looked online including China Airlines website, but when I asked BA via email if that was the case, they said that they couldn't tell me if they would through check me and my baggage or not.
I then asked BA via Twitter and they got back to me saying that as I had a connection with China Airlines, I would need to re-check my baggage and myself at LHR (Quote - "Checked baggage needs to be checked-in with each airline, even if all flights are on the same booking and ticket number") My problem is that I probably won't have time to re-check in LHR especially if I need to collect my baggage, change terminal then check-in again.
.
Does anyone have any experience of this and what do you think will happen?

Cheers