The administrator of our retirement account tells me I will not be allowed to participate in the 401K plan for six months if I take out money early for a primary residence purchase.
Can this really be true?

Yes, I've seen similar provisions in other plans.

You say you are taking "out money early" from your 401(k), but I hope what you mean is you are taking a loan out of your account, as opposed to taking an early distribution - correct?