Totally depends on the market. For example, most e-commerce companies are very comfortable using SaaS and Javascript snippets nowadays, but if you try to pitch SaaS to a bank, they'll just laugh. Over time, I think more companies will get comfortable with SaaS, but it will take years.
If you're pitching SaaS to an industry that doesn't usually go for it, it sometimes it helps to avoid PII. Even banks are somewhat open to using SaaS for products that don't touch customer's names, transaction info, etc.
I have a different problem than PII... my product will contain detailed configuration information about the customer's entire system. That makes it security-sensitive. Data will be encrypted at all times, but there's a psychological problem of having configuration information in a SaaS system at all.
Good comments, plus, if you can do it, it might be wise to have a version of your product that's not SAAS. A self-hosted version, like Github Enterprise.
Be careful, though, self-hosted customers can be huge PITA's.
It's already in the business plan, albeit in a vague way. One of the big advantages of SaaS is that I can practice Continuous Delivery and be constantly improving the product while I sell it. Besides PITA customers (a problem that can be mitigated with an install process that Does Not Suck), there's a problem of supporting increasingly obsolete versions in the field.
If you're pitching SaaS to an industry that doesn't usually go for it, it sometimes it helps to avoid PII. Even banks are somewhat open to using SaaS for products that don't touch customer's names, transaction info, etc.