I used PJ-1 Black Label for a number of years and yes, it seems to stay stringy and it does get thrown off of the chain.
I have no doubts it does an excellent job of lubing the pins, rollers and side plates but the crap on my engine and rear wheel isn't something I like.
For that reason, I've switched to PJ-1 Blue Lable.
The can says it is designed for O-ring chains because it won't damage them but it also works fine with the old standard non-O-ring chains.
The Blue Label lube also goes on watery thin and it then dries to a really thick, clear, paste like substance.
It does not form the strings that the Black Label stuff does and it doesn't seem to get thrown off of the chain all over my engine and rear wheel.
After many thousands of miles using the Blue Label stuff, I'm a happy camper.