Sorry I don't understand PEM. Sleep disorders are extremely common and can cause symptoms that may be mistaken for ME, certainly by UK doctors. It's also possible that treating the sleep disorder allows healing in milder cases of ME. I know that when my sleep improved so did other symptoms. It didn't produce a dramatic improvement but a slow change that eventually allowed me to, for example, read these forums and find other things that might help.
Post-Exertional Malaise means getting very sick a day or so after exercise, usually lasting days or weeks. The International Consensus Criteria describes it as:
Characteristics are:
1. Marked, rapid physical and/or cognitive fatigability in response to exertion, which
may be minimal such as activities of daily living or simple mental tasks, can be
debilitating and cause a relapse.
2. Post-exertional symptom exacerbation: e.g. acute
flu-like symptoms, pain and worsening of other symptoms
3. Post-exertional exhaustion may occur immediately after activity or be delayed by
hours or days.
4. Recovery period is prolonged, usually taking 24 hours or longer. A
relapse can last days, weeks or longer.
5. Low threshold of physical and mental
fatigability (lack of stamina) results in a substantial reduction in pre-illness activity level.
The pain is quite a bit different from the localized muscle pain which normal people feel after exercise. If you do crunches with PEM, you'll probably end up with your full body hurting instead of just the abdominal muscles which were used, for example. It can be hard for people to initially pin down what is causing those sorts of symptoms - in many cases, it is blamed on viruses at first, or just being "fatigued".
If someone doesn't have that symptom, it's a lot more likely that they've been misdiagnosed.