Actually it is complete opposite - if your flash lasts for time long enough 1/250s is perfectly possible (that's why with continuous light you can use any shutter speed, because it lasts long enough).
Let me explain now - when you have SS set to 1/180 or lower, second curtain starts to close after the first curtain is fully opened. So let's say we have very fast flash - sequence looks like this:
1. First curtain starts to open
2. First curtain opens fully
3. ZAP - flash just had been triggered and it lasts 1/2000s
4. Second curtain closes
With SS set to 1/250 :
1. First curtain starts to open
2. Second curtain starts to close after 1/180
3. First curtain opens fully
4. ZAP - flash fires for 1/2000s (but a small bit of flash is already covered that's why we have thin black bar)
5. Second curtain closes
If we will set SS to 1/250 and rear curtain flash we will have:
1. First curtain starts to open
2. ZAP - flash fires for 1/2000s (but a small bit of flash is already covered that's why we have thin black bar)
3. Second curtain starts to close after 1/180
4. First curtain opens fully
5. Second curtain closes
Basically black bar should be at the top or bottom of the frame (in panoramic view) depending on the sync type - whether flash is triggered after first curtain is fully open - scenario 1 - or right before the second starts to close - scenario 2).
Now let's think about hypothetical flash which lasts for 1s:
With SS set to 1/250 :
1. First curtain starts to open
2. Second curtain starts to close after 1/180
3. First curtain opens fully
4. ZAP - flash starts
5. Second curtain closes
6. Flash stops
We still have black bar
If we will set SS to 1/250 and rear curtain flash we will have:
1. First curtain starts to open
2. ZAP - flash starts
3. Second curtain starts to close after 1/180
4. First curtain opens fully
5. Second curtain closes
6. Flash stops
Only in this hypothetical situation we end up with fully exposed frame.