HI there! While I have accessed this web site daily to look at the pics of puppies (much to the amusement of my husband), but I was compelled to register this AM in order to post a reply to your topic!
My parents have been breeding Border Terriers since before I was born 34 years ago, and my sisters and I had the privilage of growing up with more than a hundred adults and puppies. We have breed them, whelped and weened them, travelled with them, shown them, lived and loved them all of our lives. Borders are clever, inquisitive, energetic, loving, loyal little characters. Border Terriers were breed for hunting foxes and other vermin and would keep up with a horse while still being able to bolt off in chase of its catch. Hopefully that one line will give you an idea of the amount of focus, attention and energy that can be contained in that little body. Nowadays they are a more versitile dog. Some of our pups have gone on to be working dogs on farms, a large portion have become a new member of families with children and a few are more than happy being papmered as lap dogs. The one thing they have all had in common is that they are clever and LOVE people. I can imagine your description of the the dog "searching", looking for a familiar face, and it saddens me. We have fostered and adopted Borders in the past with less-then-stellar prior residences, and with love, encouragement and exercise/stimulation (they are terriers!) they have made remarkable turn-arounds and have gone on to great homes.
While I don't claim to be an expert on this breed, rather someone with a lot of experience with them, I have not heard of a restriction or identification as a "Dangerous breed" being applied to the Border Terrier in Canada, US or the UK (where they originate). In saying that they are a terrier and I believe that any dog has the potential to get very stressed or have a really bad day and should be treated with respect due to this.
I hope that this helps and if you are looking for more info on the breed please look up the Border Terrier Canada, Border Terrier Club of America, Border Terrier Club of Great Britian websites (or anything written about them by James Harriot for a personal touch). I have no affiliation or membership in these clubs/associations, just know they are a great resourse.
Good luck to the little girl you met. I'm sure that she will make a fabulous companion for some one!