I'm with Mac on this.

Of course you can improve your sense of rhythm by practice, you can also eradicate any flaws if your careful about your practice.

One useful skill is knowing where you are in a song. The way I learnt this was by counting:
1234, 2234,3234,3234,......12,2,3,4 (or similar) over songs I heard on the radio in my car. I tapped my foot. I wanted to ensure that I always knew where the one was and also where I was in the song in terms of bars. Now its internalised, I don't have to count and I know which bar and which beat I am on - this intitially took a few months.

There are lots of 'away from your instrument' excercises you can create too, for example listen to a song and count every third beat, or indetify the fifth bar without counting.

All this stuff about some people have and some have not... some work at it and some dont

And BIAB is a great training aid for this - you can slow down as much as you need.