If I had to hazard a guess, it would be nothing as simple as targeting SDI as an early adopter of online courses, etc.
I would put my money on nothing more than good old dirty laundry. Someone pissed off someone else somewhere along the line. Instead of saying "We will not take anyone certified by Person X or Shop Y," they essentially decided that "We will not take anyone certified by the agency that Person X or Shop Y is working with."
Failing, or course, to see that their website will be seen by many people not locally certified, or seen by many familiar with the certification standards that they were pretending to quote...
Even with their current wording that "All participants must be certified through an internationally recognized and accepted Scuba Training Agency.
The Captain and Crew reserve the right to assess the abilities of any and all divers aboard the boat and deny dives to those who do not meet the mimimum proficiency and standard of training required for open water diving," they do not specifically reference RSTC, etc. I would be very interested to see what they would say now if you presented an SDI O/W card showing you were certified by that "Person X" or "Shop Y" (whoever that may actually be). I would also guess that if the person or shop that they are pissed of at changed agencies, then the ban would have been expanded.
I have never been to Pensacola, nor am I at all familiar with the local charters, dive shops or instructors there. This is all just my guess as to the most likely backstory...