Ok, two things wrong with this statement. One, your company will not be fined into oblivion for using the term engineer on the employees that do not hold valid P.E.s because the law specifically states that anyone working under the direction of a licensed engineer (within their field of focus) can be referred to as an engineer without fear of repercussion. Your company has valid P.E. holders on the payroll and this can even come into play if the company just hires a P.E. to stamp drawings/designs for a specific project, but it is only in context to that project. This is a standard statute in almost every state as far as I know (I am most familiar with my state obviously, but in my Engineering Ethics course this was part of the basic curriculum).
Two, and this is more relevant to TFA, the term engineer is only restricted when used in a publicly funded project or setting related to public projects. Engineer can be used for private projects and companies as long as it doesn't involve public funding or projects/infrastructure in general. This is where the guy got into trouble. He emailed the public engineering board about a public project/public infrastructure claiming to be an engineer with an issue. By the state laws he is misrepresenting himself as an engineer within context to what he is talking about.
I, as a software engineer, can legally talk about how shitty or great I think private entities programs/sites/apps/whatever software related thing and refer to myself as a software engineer as long as it doesn't have crap to do with public projects or public funding. If I start doing that with public stuff I can get into legal trouble (though this is a grey area for software specifically since the software P.E. is only 3 years old and it is still not well defined from what I understand how their stamping even works). I can complain all I want about those public projects or infrastructure as long as I don't claim to be an engineer. Again, if I am working under a licensed engineer this changes, but that also has to be spelled out and clear that I am not the license holder.
The last exception is if you are working on obtaining a P.E. or you hold an accredited engineering degree from a recognized university. You can then be referred to as an 'Engineer in Training' or 'Engineer Intern' if you have passed the first exams or as a graduate engineer respectively. This does not apply to non-accredited engineering degrees however (accredited actually varies state to state too if I remember correctly, some states require that the degree is ABET accredited to qualify for that distinction, others allow any recognized University degree to qualify for it).
Basically, these are laws designed to prevent joe blow from designing bridges or other things that the public relies on and funds without actually being qualified. It is the same idea as someone not wanting some jackass that watched a youtube video to attempt surgery on them or a loved one.