I've worked with India Indians and those I've come in contact with have also had very thick, near-unintelligable accents. I hate to stereotype, but out of the dozen or so I've spoken with, I've rarely been able to understand more than half the words spoken.
I don't have enough contact with other foreigners to make a decent comparison. The two foreign exchange students I knew in high school spoke with English accents, but they enunciated very well and were quite understandable. The Indonesian I know started out with a really wretched accent but it improved quite rapidly over the time I knew him. When I last saw him, you could still hear an accent but he was as understandable - heck, even more so - than someone from the Deep South. :=)
Bottom line: I don't know what the hell it is that makes some people adopt and speak foreign languages more readily than others. I would probably get a polite reception (but hidden smiles) if I went to Germany and tried to deliver my mangled German - but then I've never lived or tried to do business in Germany.