The term "basket pipe" gets used too widely to describe any pipe at a reasonable price, even name brand good ones like Dr. Grabow, Kaywoodie, and some Savenelli. The term, properly used, designates only pipes in a pipe shop sold out of a basket. These can include the lowest grade briars and other woods with soft plastic stems that chew through in a few months or weeks of use, but also any pipes the shop feels have been around too long, hence some quite nice ones like Savenelli unfinished pipes, and lower priced pipes from brand names. Basket pipe doesn't give a precise evaluation of their quality, only that they have been put on discount. Traditionally, if you knew your pipes and combed through the basket pipe basket on a pipe shop visit, every few visits you'd find a really good buy in a standard quality pipe, and sometimes a sweet deal on a better than standard pipe, depending on how good your eye is.
Okay, now to the present. Basket pipe is a term used to often designate pipes that are of notably poor quality that even beginners should avoid. They are poorly drilled, of cheap materials, and not designed to make a pipe smoker, a friend or a customer out of the purchaser. Buyer beware. The good old pipe shops still have baskets with real basket pipes, and some terrific deals for experienced pipe smokers and newbies who have done their homework. Just shop with your head, not your heart and your hopes.