Is a graduate student research grant an 'intent to earn money' or not?

No, what kind of form are you entering?  

Q. Is a graduate student research grant an 'intent to earn money' or not?

A. Not. Or more accurately, usually not.  It depends on the details.

The purpose  of that question is to see if the income is subject to self employment tax (SET) as well as income tax. SET is how the self employed pay their social security and medicare tax (FICA). 

An example of when a research grant is subject to SET (and is an intent to earn money): a for profit company funds your research and uses the results to make improvements in their profit making business. 

That's why it matters on what form (1099-Misc, 1099-NEC or other) the income was reported on.  If it is self employment income, the expenses of the research are deductible.