Vonage introduced this service a few years ago, as a way to offer a somewhat pared-down feature set, using an inexpensive, commodity ATA, at a lower price point than their original, Vonage-branded service. I was a Vonage customer for several years, and the service was excellent. However, Vonage (and Basictalk) offer unlimited* service, and to protect their service from abuse (sharing your service with somebody else and only paying for one user), they lock down their ATAs and don't give out SIP credentials.
So, no, they don't offer BYOD service, and thus, Basictalk can't (legitimately) be used with an OBi device.
*unlimited meaning, within their reasonable use policy.
The only other issue I had with them, was, at least where I live, my city imposes a rather high tax on utilities, and adding that to the state sales tax, and the USF fees, would raise the Basictalk $9.99 / month price to around $13-14. The full Vonage price plans also used to add some other non-mandated fees that, added to the taxes and USF fee, resulted in around a $10/month burden on top of the service rate. I don't know if they still do that, and it looks like they don't for BT.
BTW, the ATA provided for BT is the Grandstream HT-701. I use one with my ancient 1947 Western Electric 302 rotary phone, with a touch-tone converter retrofit in the phone, and it works great. It's a simple, reliable, low-cost ATA.
