OMG oops, sorry, they sounded legit when I clicked the ad. Just ignore this one then.
On that same token, I didn't look them up any further than looking at their website, which mentioned nothing that sounded vanity publishery. Oh well. Nevermind. I did think after the post that I should check preditors and editors, but I'd already posted by then...
I also think it's worth noting that sites like LuLu and amazon's CreateSpace are also vanity publishers, in my view anyway. Anything where you're paying a fee to have your book in physical form is vanity publishing, even if it goes by a different name (I'm looking at you Print on Demand).
I'll deal with these separately as it is important, on a public forum, to be clear and accurate:
Vanity publishers are often very good at making themselves not look like a vanity publisher on first glance. It is how they get their business.
Vanity publishers are places that charge you to produce and publish your book, which you could also do free. They charge you an amount of money for books and services, you do not produce the product and you will not gain any profit from selling it.
Print on demand is ENTIRELY different and in no way vanity publishing, or linked to it. You pay nothing to a POD publisher unless you purchase copies (lightning source is different as they distribute the book wider and have some set up costs). You purchase copies at cost and sell for your own, chosen, retail price. This is what authors have been doing with book printers for years - and no one calls approaching a private printer and paying to have your book produced for an agreed cost price vanity publishing. They call that self publishing.
So, to be clear: vanity publishing requires you to give money to a company to produce a product that they gain profit from. They charge for services such as editorial input, cover design, production costs and lots of other lovelies.
Print on demand services require you to pay to produce physical copies of a book you have produced, had edited, had a cover designed for. They charge a fair cost price, comparable to most printers.
The key difference is one charges a fee for services, one charges a cost for an agreed product.