That is exactly how I understood it, and what I was told a couple of months ago by a BT person trying to get me to upgrade to Infinity.
Oh come on!!
Sales people working for companies will try to talk you into buying their own services or upgrades or whatever they want you to buy.
e-on will talk you into upgrading for their dual fuel services.
Epson's manuals will talk you into buying Epson inks only.
BT will talk you into upgrade to Infinity.
Nikon, Canon, etc., etc., their manuals will tell you to buy their brand lens.
If there is something wrong with your car and it happens to be Ford, chances are Ford will suggest you take it to a Ford-approved garage and get Ford parts.
Need I go on?
I don't think you have to upgrade to Infinity, if you're a BT customer, then you're a BT customer, regardless of which of their services you use, as far as I know, there's no such thing as you have to be an Infinity customer to qualify as a BT customer.
As far as I can see, either....
If you are a BT Broadband customer (regardless of which of their range of services you use) then you get to watch BT Sports free.
If you are not a BT Broadband customer (even if you use BT just for using the phone while you use a different company's broadband), then to access BT Sports on Sky, you just pay extra to get BT Sports package included in your Sky.
As far as I can tell, if it is listed in Freeview, then maybe either a decoder or phone up BT and pay for PIN to key in for 24hrs access on Freeview. (That part, I could still be wrong, but why else is it listed in Freeview?)