If you are going to attract the attention of governments (PSN and Sony hacks, etc), yes, don't expect a VPN to shield you.
If you're pirating a show that isn't available in your region, or checking up on an old workplace website, etc, a VPN is likely perfectly fine and will save you from legal scare letters, an old employer seeing your visit, etc.
Only justification I could think of is a strict reading of CFAA, where in your exit paperwork the employer commands you not to access any company systems, and the Web site is technically a company system. Though “protected” would be quite arguable there.
I occasionally have crons from my personal infrastructure running into an employer for operational purposes (offsite monitoring or whatever), so I’ve blackholed outgoing traffic to former employers to be on the safe side in case I miss one. So I can see where that sentiment is coming from, though I think it’s a legal stretch.
So for the 99.999999% of the rest of us who don't use personal systems to provide monitoring services this argument doesn't apply. Seems like it would be easier to just use outside monitoring or setup some monitoring instances in the cloud that your employer owns than going through this effort.
If you don't like the employee example, think, "reading your ex's blog." You might want to read it but not advertise to your ex (through traffic logs) that you're reading it.
If you are going to attract the attention of governments (PSN and Sony hacks, etc), yes, don't expect a VPN to shield you.
If you're pirating a show that isn't available in your region, or checking up on an old workplace website, etc, a VPN is likely perfectly fine and will save you from legal scare letters, an old employer seeing your visit, etc.