I thought Paramedics [missed the plain clothes!] were moving Roth to the hospital after Roth's wife, Marcia presumably called for assistance

You are right Turnbull All those little gifts to the President came in handy! indeed
Roth's sequence of events – stroke “plain clothes guys moving him to the hospital, military detachment charging into his hospital room” - were constant watching / protection by Batista's BRAC and Military

Tom told Michael at the Desert Inn -
“Roth got out on a private boat, he's in a hospital in Miami He had a stroke but he recovered okay”
“I think Fredo got out He must be somewhere in New York”

What would be our ongoing re-vamp, re-visit 'revolving door'! [what's new?!] take as to how Roth and Fredo - after Batista resigning, leaving the city immediately and being caught up in the midst of the rebel uprising - got out of Havana?
1. Roth “after having a stroke and nearly being killed by Buscetta”
2. Fredo alone “walking in a daze”