Please stop making endless replies without giving it a thought.I mean, sounds like bad devs to me. Every achievement should list specifics of progress where applicable. If there's a race you haven't done, it should tell you. For the exact reason that IF anything bugs out, and it will for someone, at least then they know where to look to solve the problem.
In its current form, it naturally tells you what is missing because your save file is the trophy progress. However, if you allows the offline progress but not allows the offline progress to be registered to the actual trophy progress, you either needs to display both save file progress and server progress on the basic UI right next to each other (resulting in bloated screen), or make a switch/filter to flip between the two (resulting in confusing UI and useless to most people), or implement the feature to check the server progress on some other menu (hard to find, no one expect such feature, thus people may not find it), to let users know about their trophy progress.
What do you think what most game devs would do? They just don't show you (other than the basic progress bar which is supported on PS trophy system 182/190, which is useless to players who got a bugged out trophy). In other words, your 'solution' is not the same thing as online saving.