No, they're not. Sure, in more familiar scenarios where you're measuring the size of some amount of data it's an integer, but there's nothing mathematically wrong with having a not-integer number of bits.
See: https://en.wikipedia.org/wiki/Shannon_(unit)
If you do any sort of calculations with information theory you're quite likely to end up with a non-integer number of bits, and there's nothing wrong with that.
Just because physical hardware is more or less restricted to integer bit quantities doesn't mean fractional bits aren't a useful concept.
He was going crazy over a file being shown as 600Mb on Windows and 629Mb on mac. When he compared the bytes values, they were the same (around 629,145,600 bytes) and that settled it.
My MacBook Pro's internal "1 TB" disk is actually 1,000,240,963,584 bytes -- neither 1 TB nor 1 TiB.
To be fair: It make sense to measure RAM in MiB, because it is addressed by binary address lines so you always end up with a power of two.
Files are, however, as big as somebody decided to write into them (modulo some rounding to the next sector, depending on file system implementation details). It does not make much sense to measure them in MiB. Quite often it just more confusing to calculate file sizes in MiB instead of MB. I dont even know why Microsoft stated that MiB business.
Similar with hard disks by the way. They contain as many sectors as the manufacturer was able to put on them. There is no power of two involved.
I believe the reason is that all storage devices are marketed in decimal sizes anyway.
mb is short for millibit, the abbreviation for megabyte is MB (or MiB if you mean 2^20 bytes). I know it's a minor thing, but "m" and "M" does not mean the same thing, neither does "b" and "B", and they're mixed up too often.
Sorry for the off topic.