I can see why someone would think there was Terrier, but I'm not so sure about Basenji. (The only way to know for sure is to do a DNA test.) Both of your dogs look very similar. What breed, or mix, is the older one?
We also have a possible Basenji/Terrier (Yorkie) mix. I've had some doubts, but seeing this picture of Rosie, I can't help but see my Rebel. Such a great looking dog, and if she's anything like our girl, you're in for a treat!
So pretty and unique; glad that you ended up getting him and hopefully he never has to find a new home again…moving and being displaced really can mess with a dog (or anyone for that matter)...hope you have many years of great fun and mischief.
The traits you described are also found in most of the Nordic/spitz type dogs. I don't see anything overly basenji-ish about him in the pics. What ever he is, he's very hansome.