If my employer reimburses me for college tuition up to $5250 a year, can I still claim a education tax credit?

No, because your employer can provide $5250 in college tuition to you tax free, you cannot use the same expenses for the college tax credits.  (This is what "they" mean by double dip")

By law your employer can only give you $5250 maximum, tax free. If your tuition was less than that, and you employer reimbursed it all; you cannot claim an education credit. You do not even need to enter your 1098-T. You have nothing to claim.

 If you got more than $5250, the amount above $5250 is usually already included in box 1 of  your w-2 as taxable income.  Since you have essentially paid tax on that part, it  is considered your after tax money and that amount can be used  to claim the tuition credit.