Platinum providers buy a certain (significant) amount of Allergan products, including Botox Cosmetic, Juvederm Ultra (HA filler), Latisse (pharmaceutical for lengthening eyelashes), and Natrelle breast implants. Buying significant amounts of a product does not necessarily correlate with skill or expertise in use of the product, but generally it does, since the more you use for your patients, the better you get at satisfying those patients.
You can think of this as a sort of "Good Housekeeping Seal of Approval;" just because a certain brand of toaster, for example, has the GHSof A doesn't guarantee that the particular brand of toaster is "the best," it at least ensures that the toaster meets certain guidelines and has a "reasonable" chance of living up to your expectations. The same is true of Board-Certification, membership in professional societies, and the like!
The short answer to "Should I go only to a Platinum doctor?" (assuming there is a choice among multiple providers) is: "Yes." And the answer to "Do doctors pay to join?" is "No," unless you consider that to achieve a certain level you must purchase a certain amount of product. But, you cannot just pay for Platinum designation.