The dispute centres on "accruing resources".
This means money gathered by departments, such as farm subsidies or Housing Executive rents.
The finance minister's claims were in a memo to Executive colleagues.
In it, she warned that if Stormont cannot agree a budget and a civil servant takes control he would be legally prevented from spending any accruing resources, leading to huge cuts.
However the finance committee said that while it may be "inconsistent with normal practice", it would not be unlawful.
The committee chairman, Sinn Féin's Daithi McKay, has written to Mrs Foster summarising the advice.
The advice says that the Department of Finance can direct the use of accruing resources even in the absence of what is called the Budget (No 2) Act.
That act is the piece of legislation which puts the budget into law.
Even if the committee's advice is correct, Stormont's budget would still be sharply cut if the senior civil servant has to step in.
The permanent secretary of the Finance Department, David Sterling, would be required to impose a budget which would see every department's cash allocation fall by 5%.
Mrs Foster has previously said this would mean spending would fall by more than £600m in order to balance its books.
A so-called black hole would be created because loans offered in the Stormont House Agreement depend on the welfare issue being resolved.
There are no indications that she would bring this level of cuts forward.
The paper also presented an even bleaker picture in the absence of any budget being agreed and passed by July.
Then Mr Sterling would take control.
Mrs Foster, in her paper, stated that under legislation, income received such as planning fees and EU farm payments could not be spent.
She said this would leave Stormont facing a £2.8bn shortfall.
A spokesperson for the finance department said:  "The department will endeavour to respond to committee correspondence within the normal guidelines for responding to committee requests."
Stormont's Finance Committee has said it has received legal advice contradicting Arlene Foster's claim the executive would face more than £2bn in cuts if a civil servant has to take control of the budget.