Here’s a recent, specific and relevant example of the opposite being true - when a contract was imposed on the railway unions an amendment was sought to add sick leave. It was voted down by the republican majority. The railroad unions were left with one day of sick leave in their contract.

“You can damn well believe our members will remember which politicians supported a basic, common courtesy of a sick day when they go to the ballot box”. - Clark Ballew. Teamsters Rep.

What the Teamsters are saying (as you alluded to) is that no party is reliably supportive of Unions. Evidenced by the fact that the PEB was convened by a Democratic president.