Early on in Hyde Park on Hudson, after losing the security guards and stopping his car in a beautiful field of purple clover, FDR (Bill Murray) gets a handjob from the dowdy and somewhat innocent Margaret “Daisy” Suckley (Laura Linney).

After the encounter, Daisy’s narrative voice lets us know that now she and the president were “not just fifth cousins but very good friends.”

And that catches the understated comedy of Hyde Park on Hudson, which was a surprise screening at the Savannah Film Festival on Wednesday night.

Richard Nelson has ably adapted the script from his play of the same name — one that assumes a degree of physical intimacy that can’t really be confirmed by the trove of documents that became available after Suckley’s death in 1991 at age 100.

But I found it pretty easy to set aside the facts, since we’ll never know them anyway.

Linney’s Daisy is warm and self-effacing on the one hand, but prideful and jealous on the other. If she seems too old and staid for an affair with a president — she’s no Monica Lewinsky! — then it’s worth keeping in mind that the real life Daisy was over 40 when she began her alleged affair with FDR.

Bill Murray is pretty much brilliant as the polio-stricken president. His almost complete inability to use his legs dominates many of the film’s visuals, although the characters rarely talk about it. Those different times are wonderfully captured by the gaggle of press, Hyde Park servants, and various other hangers-on who just don’t mention FDR’s disability.

With cigarette in hand and head rakishly cocked as he sits in his car, Murray occasionally looks just like those FDR photos that we all know. He’s strong at some moments, wise at others, and sometimes bossed around by the powerful women with whom he has surrounded himself — his mother (Elizabeth Wilson), Eleanor (Olivia Williams), and his assistant Missy (Elizabeth Marvel).

Much of the plot centers on a Hyde Park visit in summer 1939 by King George VI and Queen Elizabeth (the Queen Mother). Samuel West and Olivia Colman are simply a joy to watch — and to hear — as they negotiate the vaguely functional dynamics of the Hyde Park enclave while at the same time trying to maintain their dignity and muster support for the British cause. World War II would begin in a couple of months — and everyone knew.

And I suppose one could criticize the lightheartedness here as discordant with the horror already occurring across Europe. But I’m not going to. When the king refers to the fascist assaults on Spanish civilians, the grim present and grimmer future are right there on the surface. Hyde Park on Hudson is similar to many films about distant families and friends gathering for awkward weekends, but in this narrative the participants also have to worry about saving the free world.

And then there’s the hot dog picnic (I’ve embedded here a pic of the menu from the FDR Library), which serves both as an affront and opportunity for the royal couple.

One of the best scenes comes the night before that picnic, when King George and FDR share a few drinks alone in the study. We can’t know that they found a certain kinship over their respective stutter and paralysis, but it’s a warm and human moment.

It’s worth noting, too, that Hyde Park on Hudson is a visually ravishing film — the set designs, the colors, the nighttime scenes are all immensely satisfying to watch.