That is what I remember learning years ago. I don’t have a source off-hand, but I can try to find one, if I have a chance. I think the source may actually be the Gemara you quoted. I remember learning that the Gemara is is not referring to someone who says Hallel every day, but rather to someone who says Hallel on a regular day (meaning a day that does not call for it). It wouldn’t make sense otherwise – if somone says Hallel every day of his life but one, this Gemara would not refer to him??!!
In any case, if I have a chance, I will try to locate sources.