Is my wife still considered "covered by a retirement plan" if she did not participate in her employers 401k plan in 2015?

I think it is the employer's screwup.  The employer should not have checked Box 13. From the IRS:

https://www.irs.gov/Retirement-Plans/Are-You-Covered-by-an-Employer's-Retirement-Plan%3F

You’re covered by an employer retirement plan for a tax year if your employer (or your spouse’s employer) has a:

     Defined contribution plan (profit-sharing, 401(k), stock bonus and money purchase pension plan) and any contributions or forfeitures were allocated to your account for the plan year ending with or within the tax year ;

    IRA-based plan (SEP, SARSEP or SIMPLE IRA plan) and you had an amount contributed to your IRA for the plan year that ends with or within the tax year; or

    Defined benefit plan (pension plan that pays a retirement benefit spelled out in the plan) and you are eligible to participate for the plan year ending with or within the tax year.

Box 13 on the Form W-2 you receive from your employer should contain a check in the “Retirement plan” box if you are covered. If you are still not certain, check with your (or your spouse’s) employer.

Furthermore (also from the IRS):

https://www.irs.gov/Retirement-Plans/Common-Errors-on-Form-W2-Codes-for-Retirement-Plans

Form W-2, Box 13
The “Retirement plan” indicator in Box 13 shows whether an employee is an active participant in your company’s plan. If this box is checked, it lets the recipient know that depending on their filing status and modified adjusted gross income, they may not be entitled to a full deduction for their traditional IRA contributions. You should check the retirement plan box if an employee was an “active participant” for any part of the year in:

    a qualified pension, profit-sharing, or stock-bonus plan under Internal Revenue Code Section 401(a) (including a 401(k) plan).
    an annuity plan under IRC Section 403(a).
    an annuity contract or custodial account under IRC Section 403(b).
    a simplified employee pension (SEP) under IRC Section 408(k).
    a SIMPLE retirement account under IRC Section 408(p).
    a trust described in IRC Section 501(c)(18).
    a plan for federal, state, or local government employees or by an agency or instrumentality thereof (other than a 457(b) plan).

Active participant
Generally, an employee is an active participant if covered by a:

• defined contribution plan (for example, a 401(k) plan) for any tax year and is credited with any contributions or forfeitures, or
• defined benefit plan for any tax year that the employee is eligible to participate

If she did not participate in her employer' 401-K plan, she is not covered by a retirement plan. 

Not sure why, but box 13 on her w-2 is checked.  Do I need to have that fixed?

If her employer contributed to the plan, but she did not, it is still considered to be participating.

Ok, neither my wife or her employer contributed to the 401k in 2015 (401k has a zero balance).  But box 13 is checked.

I would suggest you to contact your employer for verification.

I believe the employer is supposed to check Box 13 if the 401k plan was available, but the employee can be considered not covered by a retirement plan for IRA deductability purposes

Thanks.  We did contact my wife's employer to have her W-2 corrected and they immediately refused to modify it, stating that box 13 should be checked.  They said the IRS does not use the Box 13, but they would look to the related field that shows contributions ("D") to determine if you actively particpated.  Guess I'll polish up my boxing gloves for the inevitable battle with the IRS.

As I indicated in my previous comment, I think your employer is correct and I think you are entitled to take the deduction.  Is Turbotax refusing to allow it?

Once I check the "retirement plan" in box 13 TurboTax automatically assumes that I'm an active participant and makes my IRA contributions "nondeductible."  I haven't figured out how over-ride Turbotax (aside from unchecking the retirement plan box).  Any suggestions?

Intuits professional software looks at that Box 13 check to determine if you were covered by a retirement account.  I would  assume that TurbotTax does as well.

The IRS goes by box 13 Retirement plan.

See Zbucklyo's answer.  If the employer provides a defined benefit plan in addition to the 401(k), this could be the reason that box 13 retirement plan is marked (even if your wife does not meet the vesting requirements).

If the box 13 marking is truly incorrect and the employer refuses to correct it, the only option is to submit a substitute Form W-2 (Form 4852).

Thanks dmertz, I like your suggestion.  Unfortunately 4852 does not cover box 13.  Do you think rows 9 & 10 on form 4852 could be used to describe the issue?

I hadn't considered that Form 4852 does not explicitly provide for correcting box 13 markings.  Yes, you would need to note the reason in box 10 of Form 4852 and enter the W-2 without marking the box on TurboTax's form.  Simply leaving the box unmarked without any explanation would trigger a deficiency notice from the IRS since they would otherwise defer to what the employer reported.  You'll need to be clear that the employer has never allocated any money to your wife's defined contribution plan (401(k)) and does not provide any other retirement plan.