> they're highly skilled former Navy machinists.
In general, no. Professional welders who do well economically typically have a few things in common that have nothing to do with their origin or education:
* They work very hard (60+ hours a week or more), usually on an hourly wage and make overtime pay/holiday pay/hazard pay
* They work either for themselves or in a small shop rather than for a large business or manufacturer. Large businesses typically cap salaries for their workers at a number high enough to attract the skills they need, but low enough to protect profits for the shareholders.
* The welders have the needed certifications or specialty skill set to meet the demand in a particular niche of the market
* They live near or are able to commute or move to an area with significant demand for their particular specialty.
The most obvious example at the moment are the welders in the oil patch (Bakken shale) in North Dakota. Many of the welders working there are working nearly 24/7, making a lot of money because oil production requires pipeline welders and the oil companies are paying lots of labor overtime to avoid any interruptions in production.
For the most part, the only qualification needed is the welding certificate for the type of welding they'll be doing. The employers don't care that you didn't finish high school or that you are an ex-con, as long as you have the paper (you passed the welding tests) and can read basic instructions you're paid a decent hourly wage.
Since there's such demand, you can work as much as you want, and since you're hourly you get overtime and holiday pay.
Another example is nuclear welders... TIG welders who are certified for welding stainless, monel, or other piping types used in nuclear reactors do fairly well. They have to have certifications in the welding types used (TIG or specialized stick, mostly) and they have to pass the basic security checks needed to work on a reactor site. Reactors need maintenance, and they aren't going away soon, so there's a demand.
The myth of welders being rich is something pushed by the various politicians who benefit from being able to say that student loan debt isn't a problem. It's true that a welder CAN make a ton of cash, but those examples aren't the entire workforce and there's always a price to pay. An underwater welder can make over $1 million in take home pay over a 5 year career that usually ends due to chronic injuries from high pressure environments that last a lifetime.