I’ve never seen a 3 finger style banjo picker play the third string with the middle finger and I’ve never done it myself. It’s either played with the thumb or index finger. I’m trying to imagine a situation where it would work but I cannot. You mentioned 2 really competent instructors and I would take another look to see if that is actually what they are doing.

I'm sorry that's what I meant. s*** I need to edit that lol

Hi,, just don’t play the index 2 notes in a row if you’re rolling eighth notes (4/4 time). Same with the thumb. Depending on the roll pattern you sometimes play the third string with index or thumb, and sometimes it’s optional which one to use,,,  just keep in mind my first sentence.

Three-finger playing is largely roll-based. Which fingers play which strings is usually dependent on the roll you are playing, but there can be some variance. The thumb is often used for the notes that players most want to emphasize, so perhaps one of the instructors was trying to accent a particular note. Those are both good instructors. You’re doing the right thing taking it slow. Enjoy!

Welcome aboard, John.

Many beginners have this question. In introductory lessons we tend to work on things that essentially have the middle finger striking the first string, the index on the second, and the thumb responsible for everything else.

In fact, you should ultimately be able to play any string with any finger. Without getting to too much detail, there are pieces in the bluegrass canon that bring the thumb to the first string - and although I know of only one piece that actually brings the middle all the way to the fifth (long story) the real lesson here is that strings don't "own" a given finger. Rather, the fingers go to the string where they're needed.

Play and practice as presented. As you develop, you'll find that it's actually quite common - even necessary - for the index to hit the third string, sometimes shortly after hitting the second.

I use both depending on where my thumb or index finger needs to be next . Keep your roll going. Roll on buddy roll on . It just depends on your next move. Sometime it’ll be index sometimes thumb. Keep at it , don’t get discouraged. I’ve took valuable information from both teachers . Best of luck .

I would suggest you get the Jack Hatfield banjo course book one. He will show you the rolls and how they vary to get the melody out of the instrument. It comes with a CD. It is a great course and will get you way the road while fully understanding how all go together. It is a great system. It's only $30 plus or minus and takes you a long way in playing and understanding. 
ken

https://hatfieldmusic.com/product/bluegrass-banjo-method-book-one-beginner/

https://hatfieldmusic.com/product/bbm1-cd-only/

As chuck97 pointed out, it's the CONTEXT that determines whether one plays the 3rd string with the thumb or the index.

There are quite a few situations (for instance, the first note of the standard tag lick) where the thumb is the default, to be used whenever one CAN, but the index can be used in its place whenever one MUST. That latter situation arises when the previous eighth note (thinking in 2/2 time here) was played with the thumb. To avoid using the same finger twice on fast notes, the index is used instead.

In EVERY example of this that I've ever seen, one will arrive at the index simply by going with the flow of a bit of forward roll that's already occurring.

For a raw beginner i tell them for now the middle finger only hits the 1st string. The index hits the second, 3rd and 4th strings ,and the thumb 2nd 3rd 4th and 5th..
I think that takes some of guess work out of it and the more complex rigjt hand work will come later
That rule of course is not written in stone but for a raw beginner who had no musical experience on guitar i think its a good way to start.

If you're playing forward rolls such as 5-3-1 or 4-3-1, which are ubiquitous in Scruggs style, the logical right-hand sequence is thumb-index-middle. That means that for those rolls, the index finger plays the third string. If you're playing a 3-2-1 forward roll, the third string is played with the thumb. If you play a four-note alternating roll such as 3-2-5-1, the logical sequence is thumb-index-thumb-middle, which means that you start the roll with your thumb on the third string. If you play a 4-3-5-1 or a 5-3-4-1 alternating roll, you use your index finger to play the third string.

The right-hand roll patterns that you need to play in combination with the strings you need to pick dictate which finger is used to play the third string. You need to learn to use both the thumb and the index finger to play the third string. In general, the objective is not to use the same finger to pick two successive strings.

But if you play an 8 note pattern such as  2 1 5 2 1 5 3 1   you can pick the second string with either thumb or index, especially if nothing came before.

Or depending on what came before.

A lot of times the youtubers/Patreon/beginner books/dvd lessons have tabs available (maybe even on-screen) and often have a T, I, or M under each note to indicate which fingering they expect you to use to play that note. This helped me very much early on. And after a while you recognize patterns, have muscle memory, and just know what fingers to use without needing to look.