There are probably a hundred other similar platitudes you could reel off in place of what's the worst that could happen. Springing to mind is nothing ventured, nothing gained which is at least a little more positive. However, most intelligent people recognise platitudes for what they are, and they are all as meaningless as each other.

Fears are often of the unknown. Your specific example, public speaking, is a good one because this does get easier with practice. There are practical steps you can take to be more prepared, and therefore more confident. Rather than use generalisations and platitudes, tackle specific fears directly by researching them and learning how to overcome them.

Fears are often of the unknown. When it comes to public speaking, experience is vital. Very few people are "natural" public speakers, for most it is a learned skill. As you point out, a person is often of interest as a speaker because of their knowledge or skill in a particular field, and they may have no speaking experience.

In my opinion there are worse situations than a nervous speaker. An enthusiastic and confident speaker who in fact knows nothing about the subject is equally infuriating. Equally, someone can be entirely without nerves yet be monotone, dry in their delivery, and humourless.

Your suggestion to have an experienced speaker interview the "expert" in their field is a good one. The interviewer can act as an "everyman" and this draws out the real speaker to deliver information in a way that more people will understand. This may also give the "expert" the needed experience of being on stage, seeing how an audience reacts, and could give them the confidence to directly deliver a talk in the future.

But to directly answer your question of how to calm someone's anxiety (presuming that they have agreed to a talk and have nerves, or need some persuading to get over their nerves) there are a few things that may help:

1. There are practical steps a person can take to be more prepared, and therefore more confident. Encourage them to write out a talk verbatim to begin with. They should practice the talk many times over out loud and if possible in the room where it will be delivered. If this isn't possible, at least practice in the same position (standing or seated) as they will finally deliver it. As they practice out loud, correct any parts of the script that do not sound right and adjust the draft. Once happy with it, they should work to reduce the script to notes with the goal of speak extemporaneously. One methodology is to use words like show, tell, explain in the margin to denote which parts you can put into your own words, which bits need to be read to get the details correct, and where you need to point to a textbook or powerpoint for example.
2. The most encouraging things you can say to reduce nerves are to avoid platitudes like "it will be fine" which only dismiss their fears, and instead focus on positives. Tell them that it is their expertise people are interested in, not their speaking ability. Put across points from my earlier paragraphs - namely that an audience will be far more interested in hearing from a genuine expert with a few nerves than someone who can speak confidently but knows nothing. Tell them that the audience wants them.
3. Many speakers feel more confident with a bit of a "comfort object". It may sound crazy, but standing in front of a crowd with empty hands can make a person feel self-conscious. You may have noticed that many teachers, lecturers hold a marker pen in their hands whilst talking, even if they have no intention of using it. A laser pointer, a hand pointer, or a marker pen can give a strange confidence boost - so even if they don't need to use it much, suggest some use of an object like this to get it into their hands and you might see a big change!
4. Although people expect multimedia presentations these days, I actually hate Powerpoint slides because non-confident speakers use these as a "comfort object" and end up just reading the slides (boring - the audience know what is coming), and worse still, facing the screen with their back to the audience. If you think this will happen, discourage their use and use handouts instead.

These are all from my personal experience, some may disagree, and I can't quote anything to back them up. But the practical stuff certainly works for me every time. I hope it is of some use here.