I agree with you, yet my brain says it feels different, sub is in near field but still I know it shouldn't matter
What is your sub? Grills do make small changes to measurements generally of questionable audibility.
However, I am not aware of data on subs, where it probably is significant under some circumstances. This would be especially true if it was a sealed sub, or a ported sub with the grill also covering the ports. All cloth woven grills have a definite resistance to air flow, which you can confirm by blowing though it.
In a sealed sub cone excursions are greater, as all the air movement is produced by cone excursion. In a ported sub at resonance the pressure in the box is high and cone excursion is dramatically reduced and the majority of the air displacement is from the ports, although over relatively narrow frequency band.
In my case I use transmission lines and the pressure at the speaker is high, and even with prodigious bass output cane excursion is not great as the pressure behind the speaker is high and the cone excursion controlled. This occurs over a significantly wider bandwidth than a ported reflex box. In addition the port is much larger allowing for non resistive air flow.
So I think it more likely than not, that in sealed subs, especially, the grill fabric could, and likely does cause a resistance to air flow with audible results, but I have never measured it, as I have never built a sealed sub, and never covered a sub port with fabric.
Having said that, I feel the risk of damage to speakers with grills off is high. Therefore I strongly encourage the use of grills.