Do all members of a controled group have to offer a medical plan to its employees ... just because the parent corp offers its employees a self-insured medical plan ?

I realize that a self-insured medical welfare benefit plan can't discriminate ... but what does that have to do with subsidiary employees not having medical coverage ?

I always thought that there were no "controlled group" effects, rules, requirements etc .... in regards to welfare benefit plans. (I realize that there are always important
controlled group aspects regarding retirement plans).

For insured health plans you are correct. There are no nondiscrimination rules as to coverage. (We can still be thankful that IRC Section 89 was repealled.)

But, you're dealing with a self-funded health plan which is covered by IRC Section 105(h). That section does impose nondiscrimination requirements for eligiblity (and benefits) for self-funded health plans. I don't have the Code in front of me, but in either Code Section 105 itself or in Code Sections 414(B), © and (m) (these are the controlled group, affiliated service group, etc. rules), you'll find that these rules apply for purposes of 105(h). So, just as with retirement plans, the parent and wholly owned subsidiary are treated as one entity.

Thus, excluding the subsidiary could result in a discriminatory self-funded health plan. And, if it's a large enough company, you might even be able to use the separate line of business rules (IRS Section 414®) to exclude the subsidiary without any problems at all.