You need to change your mindset on the subject. Harmful links WILL and DO affect you in Google’s SERPs. You can destroy a competitor with spammy, unnatural links, that is one cause of a Google Penalty.
Answer the question then. Is it, or is it not a HUGE flaw in Google’s search algorithm if I can run one of the many spam applications against my competitors?
It is. How else do you think people get spammy links come through on their sites, causing them problems if it can’t be done? Negative SEO is all to do with people filling up their competitors with harmful, spammy, unnatural links; affecting them in Google’s SERPs , thus them overtaking you in positions in Google.
Regardless if it can hurt your website or not, there’s nothing you can do to reverse it as the SEO company you hired earlier refuses to take the links down. Having good quality backlinks is very important. This is why it is essential that the company you hire to get quality backlinks for you should only use white hat techniques to ensure Google doesn’t penalize you. Where I work we do just that and we believe in quality backlinks over quantity backlinks.