First I'd like to clear up some misconceptions you might have about the NTRP rating scale and where players (and teaching pros) fall on that scale.
The skill level of your local tennis pro or instructor can vary greatly. Some tennis pros are former professional players while some, who understand the game and the mechanics of all the strokes, are nowhere near the 6.0 level of playing ability. Of all the teaching pros I've ever known (about a few dozen) I'd say most average somewhere between the 4.0 to 5.0 level of playing ability. It mostly depends on how often they are still playing competitive tennis vs. just hitting balls out of a basket for other people to practice. Some might be coaching college level teams/players while others are just running cardio tennis on weeknights or teaching quick-start 10 & under to kids.
As for the actress you read about (Elisabeth Shue by chance?) - I would find it very hard to believe that anyone (whether the have natural athletic ability or not) could go from a beginner to a 4.0 or 4.5 after just one 3-day clinic. Acquiring skill in tennis is a very technical task and it takes the kind of time and repetition that just can't be done in a few days. Most adults that have reached the 4.0 or 4.5 level have only done so after many years or playing and practicing regularly.
Without having seen the player or knowing the coaches, I would say you are probably correct that this player had some natural ability and reached close to the ceiling of their potential quickly. Keep in mind though that many people that play tennis never ascend above the 3.5 or 4.0 rating their entire lives.
As far as the NTRP ratings themselves go - you are correct that they are a little bit exponential but not quite ten-fold or to the degree you mentioned.
From what I've seen, the margins of victory and what separates one level of player from another gets smaller as you go up the ratings scale. For example - an average 4.5 player might occasionally lose to a good 4.0 player - maybe because the 4.0 player is more fit or has a little bit better tactics and patience (fewer errors).
A player that is a true 5.0 level player would almost never lose to a 4.0 player and in fact, most of the points would probably be pretty lopsided, with the 5.0 player being in control of most (if not all) of them. As you look at players higher and higher on the ratings scale, they do pretty much everything a little better. Better 1st and 2nd serve, more consistent ground strokes, more aggressive in finishing points at the net, better tactics, etc.
What's interesting is, as good as a 5.0 level player is - and this is often true of the game of tennis as a whole - there is always someone who is better. That 5.0 player, who might have good shots and technique, and maybe played in college, would get completely demolished by a 6.5/7.0 level professional player. A 7.0 level player is someone that makes a living playing tennis and has been playing regularly (and frequently) since they were a child. There are just different levels of fitness, balance, strategy and experience at the 7.0 level that make the difference. Not to mention all kinds of other things like muscle memory and things that get developed over the course of many years of playing the sport.
Even among pro tennis players, you'll occasionally see scorelines like 6-0, 6-1 where one player was just having a bad day and their opponent was playing well. It doesn't take a whole lot sometimes for a match to be lopsided. Even as good as someone is that's ranked say, around 500 in the world (who is a 6.5 or 7.0 level player) - someone that is in the top 10 in the world would likely defeat them easily in a match - it happens all the time in the early rounds of grand slam events.