If this is true, market share should not fluctuate noticeably, correct?
As I mentioned, although UPS is FedEx Ground's primary competition, both companies also compete against the USPS, LTL and in-house shippers. While FedEx Ground's market share has rapidly grown, neither you nor I know the source of acquisition. We do know that FedEx, at least in recent years, has conceded that SmallPost has driven their Ground volume growth. Much (but certainly not all) of the SmallPost/SurePost volume previously flowed entirely though the USPS; thus, I would assume that FedEx's recent market share gains have come largely at the expense of the USPS (does the USPS still get to claim credit for SmallPost).
Over the past decade, FedEx has invested billions into overhauling its Ground network, most facilities were built (or re-built) to accomodate growth well into the future. It'd be foolish for UPSers to pretend that FedEx Ground is going to go away. But likewise, it's foolish to persist that shippers don't shop around for the best deal (price and logistics-wise).
L.L. Bean is an example of an account UPS got back, but from what I understand you aren't making any money on them at all. What good is that?
...and you really believe that? In the early to mid-2000s, FedEx was notorious for inking low-balled contracts (Newegg, GM, etc.) but they've ended that practice, likely because many companies looked elsewhere once the introductory deal expired. I seriously doubt either company is signing contracts today that they don't feel will yield profits.