My daughter has been in a masters swim program for over a year now , and has really gotten fast. They practice multiple strokes, as apposed to only freestyle. She tells them she wants to get faster for tris, but they insist on the other strokes.
Is it a fact in the swimming world that multiple strokes improve your freestyle? If so I will add a little to my workouts.
Yes; add a little to your swim workouts.
Back in what seems like the distant past when I had the energy to do a little extra training on top of my written training schedule, I would add 5x200 IM to a couple of swim workouts each week. Much more compellingly, all the really good swimmers swim all four strokes so there must be something to it 
Really depends on time constraint actually.
If your in the pool 4+ hours a day like most elite/ncaa swimmers, your doing other stuff to save yourself from the monotony, and to build different muscle groups.
But you’ll find most elite swimmers won’t practice more than their primary and secondary strokes because there are other more efficient ways of improving those strokes other than swimming other strokes (Ex. weights, drills, resistance training, dryland). IMers of course have to practice all four.
If your only in the pool 30 minutes to 1 hour per day or swim less than 5 times per week, do about 95% freestyle.
If you’re working out for ~2 hours, go ahead and mix in drills and other strokes, but the main set should focus on your primary stroke.
As far as masters swimming, most people have the attention span of a 2-year old and want to do new things in the pool on a daily basis, and it keeps them motivated if they are doing different things. Most masters don’t swim enough to really be starting to shift out into other strokes. Until you get to a point where training all season (9+ times a week) may or may not improve your times, the best improvement for your freestyle is swimming freestyle.
I think mixing in some different strokes is great to work different muscle groups. Adding some butterfly or IM to a long set will really crank up the intensity. I also like doing some breaststroke kick to help loosen up my legs after my long run day. I do a lot of sets like 12 x 100, every 4th 100 IM or even 12 x 200, alternating 200 IM, 200 free.
I find the more stroke work I do, the better freestyler I become. This is probably only true to a point, but the most non-free I will do is maybe 20% of my total yardage.
Even if you are only racing freestyle in tris, backstroke is a good way to loosen up, breaststroke improves your feel for the water and fly helps build strength and power. IMs are great because they simulate a tri start as the fly tires you our like starting too fast or starting fast to get clear of the crowd and then you get used to recovering a little while still swimming.
If for no other reason than practicing other strokes might keep you in the water a little longer and help you enjoy your workout a little more, it would help. Just getting the extra time will help your conditioning and feel for the water.
A few things (general waffle really!):
Breaststroke can help, but it can potentially be injurous to triathletes in particular, due to the strain it puts on the knees. In addition, it uses muscles in a way that is unusual for many tri folk, and can cause issues if the person pushes to hard, and/or is not used to doing the stroke. I add that since it works the legs very hard, it may not be all that useful for triathletes.
Fly is very good, tests efficiency, flexibility, power. Great for simulating race starts, doing powerful sprints, practising beach entries and exits, beating the waves etc.
Back (as said above) is good for warm-up in terms of loosening up the shoulders, and can help newbies understand how flexible ankles would feel when they kick (compared to kicking with free).
To add to all of the above, I discovered that doing some good, hard butterfly sets made me a better freestyler. I’m not sure of the mechanism, but I imagine that it had something to do with strengthening some of the same muscles.
Mostly due to time constraints and crowding, our team has been doing Freestyle workouts for the past few weeks. On Sunday we had a 1.5 hour swim workout. We did an IM set for our main set. It was awesome! It made me control my breathing a bit more and conserve my energy in such a way that i could complete the entire main set of IM’s without blowing up. It was a challenge in different way than just swimming freestyle. I loved it! i was buzzed on the IM workout the whole day after.
IM’s are considered by many to be the 5th stroke. And also considered by many a stroke when used in training makes a swimmer tougher than nails.