More acidic than what? Primary alcohols aren't very acidic. (methyl<primary<secondary<tertiary)
Why? The more stable the conjugate base, the stronger the acid.
What you mentioned about alkyl groups donating charge is NOT as important as the CARDIO rules. CARDIO rules are a hierarchy of what to consider 1st, 2nd, 3rd... If you consider these factors out of order, by putting the alkyl groups first, you will be wrong sometimes.