Overtime is generally based upon daily overtime (in California) or weekly overtime in which somebody works more than 40 hours in a week. Holiday pay is generally a private employment benefit. Employers should have written rules about how holiday pay works insofar as on what holidays it will be paid, what the rate is, etc.
http://employeelawca.com/lawyers-for-employees/ outlines many examples of California wage and hour scenarios.
If an employer is refusing to pay holiday pay because overtime was worked the same week this sounds like the employee who was paid overtime is being treated differently and/or retaliated against for working overtime. This is not an advisable employment practice in Texas which is subject to the Fair Labor Standards Act.
Karl Gerber, Esq. licensed in California and Texas