The way I think of it. If you're "good" at long time controls (like >1 hour) then you have potential to be "good" at speed games. All you'd need to do is practice how to make use of the short time control. Cut out unnecessary analysis for example.
Agreed that a "good" speed player can't necessarily transition (right away) to a "good" player at long time controls. The reverse process of cutting corners to speed yourself up is adding analysis, and if you don't have the knowledge to begin with then it's not possible / useful.
As for ratings, remember they're not an absolute measure like how fast you can run a mile. Chess.com blitz 1297 may equal chess.com standard 1421 as long as the standard pool is generally weaker than the blitz pool. By looking at many player's ratings (and playing yourself) you can get a feel for which pools are tougher.
After playing approximately 1 year of blitz and 1 month of bullet/standard, the order for me, by rating, now stands at (1) bullet, (2) standard, and (3) blitz. Therefore, it makes me question whether there is a valid conclusion to be made about a correlation that exists between the types of chess, in regard to time control. Evidently, the principal factors to be considered here are experience (as a player with the general time restraint) and overall skill (the consistency of playing good moves, or merely one's knowledge about chess/various openings). Of course, there is no general consensus to this question, as each person's situation differs. Personally, I believe that if you are a high-level blitz/bullet player, it doesn't necessarily mean that you will be a high-level OTB/standard time control player (without considering whether the blitz play is OTB or not). If anyone stumbles upon this post, I'd like to hear your opinion about this topic. Thanks!