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At will employment means that the employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true.
Since employers are not required to have a good reason or fair reason to fire an at will employee, the law does not require them to tell a terminated employee the reason, or to honestly state that reason. So, there is nothing inherently unlawful about terminating an at will employee claiming it is a reduction in force but then hire someone else with the same qualifications. There could be a variety of reasons for doing this, including a change in the financial circumstances in the employer (i.e. things got better after the layoff), the new job being different than the one previously being performed and the employer thinking someone else might be more suitable, or it could even simply be the employer wanting to spare the feelings of the terminated employee by justifying the termination as being for cost reasons. None of these reasons are illegal.
The only way this situation would give rise to any legal claims is if the terminated employer could prove that the "layoff" was really a pretense to cover up for termination motivated by a legally protected trait or activity, as defined above. For instance, if an employee had just complained about sexual harassment (a legally protected activity) and then was "laid off" shortly thereafter, the fact the employer hired someone else with the same qualifications would tend to suggest that the "layoff" explanation they were given was really just an empty pretense to cover up the employer's true motivation--retaliation for reporting sexual harassment. Of course, you would need evidence of an unlawful ulterior motive in order to make this sort of argument. But if you think you can, then perhaps a wrongful termination claim is possible on that basis.
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