Is it true that a full Ph.D. is a disadvantage for technical positions in the private sector?
As someone with a PhD who did a regular postdoc and now works in the private sector, the answer is definitely probably not...maybe. As with all things, it depends on the job and your field.

I have a PhD in Computer Science. I did research for a couple of years as a postdoc. I enjoyed my postdoc, but a great offer came along for a private sector job. In my field (high performance computing), having a PhD is valuable whether you're in research or industry. In fact, we hire fresh PhDs as well as folks with experience.

That being said, if you were to go to a startup in NYC or Silicon Valley with a PhD in CS, I'd imagine that while you would probably have as much chance of getting the job as anyone else, you probably won't be getting what you might call "reimbursed" for your opportunity costs. The big companies will have research arms where they know what to do with PhDs while the small ones won't.

It all depends on what you want to do. If you want to get into research (or get back into it eventually), having a PhD will be a must, even if you take a few years in industry to shore up financially. However, if you don't get your PhD now, the chances of you finishing it later much smaller. There are plenty of people who do it, but if you look around your group right now, you can probably tell me how many you see.

The exception is getting a job where your employer will essentially pay for your PhD (not like an RA position where you make beans). There are some companies or research labs that will allow you to work on your PhD while you work for them, often using a project with your company as a part of your thesis if your interests align with those of your employers. You might be able to find a position like that.