Your site is as secure as the weakest link in the chain. How secure is http://www.siteground.com/ in the first place? A 13 year old script kiddie can bypass the .htaccess
of a sufficiently outdated apache. You need to ask the question: how carefully do they maintain their systems? Do they comply with the highest security standards? I couldn't find anything about this on their website, so you'll have to ask them.
It's not all about up-to-date systems. Configuration is important too. A poorly designed .htaccess
could be the weakest link as well (thinking about basic vs. digest authentication). See How secure is .htaccess protected pages.
I can't say anything about siteground specifically, but in general, you need to remember that admins are humans. Ultimately you'll have to make the decision yourself: do you trust anyone? How bad is it if your data gets out? Is it threatening Mankind? Your life? Or is it just going to be annoying? There is no single answer here, you'll have to build your own.