... one large assumption, that being that a court of law would see a customer list as intellectual property...
And I doubt any court would, as it is not in any way innovative.
However, such a document may be subject to copyright provisions, under a category known as "aggregating facts"
I dont know the copyright law in the USA well enough. But, a telephone book is an example of aggregation of facts; if in your juristiction you can copyright the telephone book, then you can copyright your customer list. Just for clarity - each individual item (a 'fact') such as a single phone number is not copyrightable in its own right, but some juristictions recognise that collecting those facts together requires effort and is in effect a work with an author, even though the content is not original or innovative. Thus they allow the collection as a whole (or in some part) to be copyrighted.
Breech of copyright is, of course, a civil offense (or is it a tort - where's a lawyer when you need one!) and damages can be awarded, and a court can order restrictions on further use.