This is the most likely situation. If a VPS provider is sufficiently cheap, it will attract the wrong people, who will then get the entire VPS provider's IP blocks blacklisted.
It's a shame, but it's the reality. There are lots of discussions around this subject on various mailing lists, where people from the likes of Gmail have chimed in stating as much.
I would reckon it takes as little as 10% of the addresses in a /24 (so ~25 IPs) to get that entire netblock blacklisted.
If you want a higher probability of clean IPs, you need to be using a provider that is sufficiently expensive to not attract spammers.
Either that, or you need your own IPs.