I book all mine on line for three with no problems every trip and then about month I call and go over them all with live CM and never had had a problem with three getting a table. It is the time that gives out the table so may be that no 4 tops at the time you wanting. one time years ago they told me Le Cellier would have to seat us at two tables as only had two 2 tops and I waited and called back and got one table for three...which was a 4 top. do not book for four and then show up with three as they will not seat you and if it is one that charges $10 per person that does not show up then your have that to pay or put on your card. that is new this year. they want a 24 hour cancel and on the signatures where you have a credit card hold is 48 hour cancel...know last fall my DBL was in the restroom at Tony's and we told her when she called us he would find us and she said no she could not seat us until he back. and then we waited 45 minutes for our table...and no DBL will never hear the last of that one
For restaurants with a CC hold (not full pre-pay like CRT, HDDR, and the like), the per person charge is only (supposed to be) assessed if you all don't show up. As long as part of your party shows, you won't be (shouldn't be) charged at all. Of course, there are still some that may slip through, so it's good practice to keep your receipts and check your statements.
The not-seating thing is more about the full party being there (everyone who is going) than having an ADR for a different number of people. If you tell them that it's only going to be 3 when they say "Party of 4", they'll have no problem with it. I've done this many times while traveling solo with ADRs for 2 (for various reasons such as not realizing I booked for 2 (stupid default), plans with Mom changed, or just for better times).
The invisible +1 person has been a method suggested by Disney for years now for groups with odd numbers of people.
I think what some people reading and posting on this might be missing is you don't ALWAYS have to pop up your party into a larger number to get an ADR. It's just a trick. I had a lot to choose from when I made my first set of ADRs back in April, but as time has gone on and I've wanted to change some stuff around or just wanted different times, the choices have gone down. I'm going solo, so no matter what I'll be taking up a table for at least 2 people (and if you're thinking "they could put you at the bar", I wouldn't take that seat, I make ADRs to ensure a table) So when I wanted to change 2 things around recently and found times I didn't care for putting in "1 guest", I tried "2 guests" and got the times I wanted. Like it's been said, Disney would rather have 2 people than 1, 4 than 3, etc etc and that's where this quirk comes in.
Solos do get hit the "hardest" with this issue

. I have had to do the same many times. In fact, I just booked a Yachtsman meal for October for 2 at 5:25pm. For 1, there was no availability until 8pm. It's some weird bug with their reservation system and has been happening since before online ADRs became available.
Of course, with solos, there's always the "The system defaults to 2 and I didn't notice the change" excuse built in

.
And yup, you can certainly find times for odd-numbered party sizes, you can usually find more and better times with the +1 even numbered group (depending on base-size and such, for parties of 1-5 or so, it's pretty consistent). There are rare cases when the real size does work better, but those are more rare than the opposite. (And this method was suggested to me, several times, by Disney Dining CMs....while they're not particularly knowledgeable about stuff, and get a lot of stuff wrong, this works so I'm going to parrot it

)