I agree Vince about the clay-lined basket theory to be dubious, but I'm also not sure that we can proclaim that fired pottery was discovered before basket-weaving.
You're certainly right in that the evidence for baskets only dates to about 8000 B.C., while we have found fired figurines that date to 25,000 B.C. However, that in itself does not mean that basket-weaving only dates to 8,000 B.C. It's likely to be older. We just don't know how much older because grasses and reeds are so biodegradable. In addition, the earliest evidence for baskets is in the "pre-pottery" Middle East. One of the confusing things here is that while the earliest ceramic pots have been found in China and East Asia, there isn't much evidence for pottery elsewhere until much later. And we need to differentiate between ceramic figures and ceramic vessels, "pots", since the former are about 5-10,000 older than the latter. Pots date from 15,000 years ago (ish ... it keeps getting pushed back and they keep arguing as to whether the small fragments found are "pots"), while fired ceramic figures have been found in Eastern Europe/Russia that date to about 25,000+ years ago.
On the other hand, direct observation of primitive cultures, as well as archaeological evidence, mostly argues that humans used tanned hides as cooking pots and bags and other items where a "clay-lined basket" sounds likely.