CARES-related withdrawal: eligible plan vs. opt-in

First, the administrator of a qualified plan (or IRA) does not 'apply' any tax, including the 10% 'penalty' for early distribution. The adminstrator does specify codes on the 1099-R for the distribution(s) such as:

 1—Early distribution, no known exception (...)
 2—Early distribution, exception applies (...)

Note the "known". Exceptions to 72(t) exist (even before COVID) that the administrator does not or may not know about. You are the one responsible for designating, on 5329, what exception if any applies, and either computing the resulting extra tax or not. I presume the 2020 instructions, when issued, will allocate a code for CARES/COVID. (And there will probably be a form, or at least a checkbox or suchlike, for the 3-year spreading.)

And the 20% withholding on eligible rollover distributions isn't tax either, only withholding -- i.e. an estimate, and a crude one compared to wage withholding, which most of the time is close to correct. When you prepare your return next spring, your actual tax attributable to this item may be more or less.

To your actual question, no the adminstrator needn't agree this is COVID-related. See notice 2020-50 in IRB 2020-28 in "Section 1" at "C. Definition of coranavirus-related distribution":

In general, a qualified individual is permitted to designate a distribution described in the preceding paragraph as a coronavirus-related distribution. This designation is permitted to be made with respect to any distribution to a qualified individual that would meet the requirements of a coronavirus-related distribution without regard to whether the plan treated the distribution as a coronavirus-related distribution. Thus, periodic payments and distributions that would have been required minimum distributions but for section 2203 of the CARES Act, received by a qualified individual from an eligible retirement plan on or after January 1, 2020, and before December 31, 2020, are permitted to be treated as coronavirus-related distributions and, therefore, permitted to be included in income ratably over 3 years. Similarly, any distribution received by a qualified individual as a beneficiary can be treated as a coronavirus-related distribution. In addition, ....

As explained in section 2.C of this notice, an employer retirement plan also is permitted, but not required, to treat a plan distribution meeting the conditions described in this section 1.C as a coronavirus-related distribution. It is possible that a qualified individual’s designation of a coronavirus-related distribution may be different from the employer retirement plan’s treatment of the distribution. This different treatment could occur, for example, if a qualified individual has more than one plan distribution that meets the requirements of a coronavirus-related distribution, but one of those distributions occurs before the effective date of the plan amendment providing for coronavirus-related distributions. The different treatment could also occur, for example, if a qualified individual has distributions from more than one eligible retirement plan, and the aggregate amount of those distributions exceeds $100,000.

As to whether the plan you're in is 'eligible', that is covered in "Background" "A. Distributions" where the list includes, stated very briefly "a qualified plan under § 401(a)". I've never heard of "Optional Retirement Plan" as a specific, defined thing and it certainly doesn't appear in any IRS publications I've read or the law I've looked at. I suggest checking your paperwork -- under ERISA you should have received at the very least a Summary Plan Description every year, and usually quite a few other required disclosures -- to try to determine if this specifically is a 401a qualified plan (or any of the others listed in the notice) and if necessary try to compare to the law (which is quite convoluted and often arcane).