I think it is a myth. First, we have to keep in mind that, generally, we have fast twitch fibers that will always be fast twitch fibers and slow twitch fibers that will always be slow twitch fibers. No amount of training will turn a fast twitch fiber into a slow twitch fiber or the other way around. There is a third type of fiber that, off the top of my head, I recall being a fast twitch fiber that can be trained to take on some characteristics of a slow twitch fiber but it's still a fast twitch fiber. Anyway, that's mostly irrelevant in this discussion because you're not turning a fast twitch fiber into anything other than a fast twitch fiber.
As for losing speed, from what I've seen, this is more about losing neuro-muscular coordination and maybe de-training the fast twitch fibers to some extent. These things can be recovered with proper training after essentially any amount of time off.
Getting past theory and physiology and into your particular situation, absolutely, you can take a break from your speedwork to build a base. You don't necessarily need to if you want to do an occasional workout or strides once or twice a week but you can recover your speed if you do. Also, absolutely, there is no need to do strides all out. In fact, doing so could be counterproductive. The goal of strides is only partly to run quickly. More importantly, it's to run quickly with good, clean form. When you run all out, you strain and may get some sloppy form. Instead, I'd prefer to see someone run more around mile race pace and focus on good clean form – no wasted motion, all straight forward and back motion, no overreaching, especially overstriding, things like that. This will be more productive in developing good neuromuscular coordination than trying to go as fast as you can, which will likely lead to some form flaws.
I've changed my suggestions for base building over the years as I've found (with the help of individuals like denton and Andrew) there is some benefit in keeping some fast running in there as long as you can control your efforts and not make the fast running into a full-fledged hard workout. The key, as it sounds like you have found on your own, is to not overdo it. Personally, I don't think strides should be a hard workout. If anything, you should feel better the day after running strides than you would if you had not run the strides. If you're drained the next day from pretty much anything you did in base building, you probably did it too hard. Take something off the strides and, as it sounds like you have found, you will get more out of all of your running.