Slightly longer comment on use of discounting OTAs for BA bookings. First off, it's almost always better to use the BA best price guarantee where it applies (I think ex UK only). You get more than the best of both worlds then and it's really not onerous. You just run through a dummy booking on the OTA and take screenshots to show details of the fare, accepted card types, as far as possible the equivalence to the BA fare class (don't worry about that), book with BA and fill in the form, sending the screenshots which must include date and time (so best done on a PC or Mac).
If you go with an OTP - for example because you're not flying ex UK - then in general you'll get a BA PNR at some point in the process of booking/ticketing. It's sometimes a little difficult to find or listed as an "airline check in code". Once you have a PNR you can manage it via the BA site and add BAEC number. You can't generally UUA but you can select seats and bags and so on. Any refunds needed have to go via the OTP, and this is the major issue, because this can take a very long time and a lot of nagging. Generally rebookings on cancellations need to go via the OTP too, and in my experience this is a little easier. Day of travel disruption can I think be done via BA or the website. Do not expect good or expert customer service when you are bottom scraping on price.
I've never encountered an OTA who is a straight up fraud, you do generally get ticketed. Doesn't mean they don't exist, but the aggregators will tend to weed them out and not present them.
My upper threshold for an OTA booking is somewhere around £80-100 if I get a substantial saving, I wouldn't go much above that for price. I have to say I use them a lot more for non BA airlines, because of the best price guarantee which is difficult to beat. One of my pastimes is creating and flying intricate itineraries with multiple carriers and the savings from OTAs are often quite worthwhile in that context. I wouldn't book a family holiday with a discounting OTA.
There are some OTA only fares incidentally. There was a Finnair Helsinki one last year which was extraordinarily inexpensive, and I bought tickets to Mulu in Malaysia for a fraction of the MH price from a discounter.