Can parents of children who are using distributions from education savings account say that they are providing support for students ?

Simple answer: yes.

The treatment of expenses paid with distributions from Sec. 529 plans and Coverdell ESAs in the support test is uncertain because of the dual nature of these college savings vehicles and  and a lack of IRS guidance.

The most common practice  is to treat a 529 or ESA distribution as parental support (or, at least support, not provided by the student*), as the parent is the owner of the plan. Making  distributions to the owner rather than the  beneficiary, or the school, would reinforce this position. 

References:

https://www.savingforcollege.com/articles/the-impact-of-529-plans-on-claiming-a-dependent

http://www.aicpa.org/publications/taxadviser/2010/august/pages/nichols_aug-2010.aspx

https://ttlc.intuit.com/questions/3402602-can-i-claim-money-from-a-529-fund-as-my-supporting-my-22-y...

*There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.  The support test is different for each type.  The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.