Given the errors you're seeing, odds are high that there is actually a problem with the drive.
In all the years I've been dealing with SMART, two things have been evident:
1. SMART is prone to false negatives – Just because SMART says a drive is OK, doesn't mean it is. Especially when it comes to physical defects of various kinds or serious controller problems.
2. If SMART says a drive has a problem, it has a problem.
So you can trust that if SMART finds a problem, it's definitely a problem but if SMART says it's OK, you have more work to do.
Same with software RAM tests like memtest86.