my fiance is currently finishing her MFT at Fresno State and I can assure you that there are paid internships available for MFTs. However, most schools require students to complete a few hundred hours before awarding the masters degree (in her case it is 600) and she does not know of anyone who has gotten a paid internship for those first few hundred hours. However, after the 600 and masters degree completion she knows some ppl who have gotten paid internships.
Keep in mind the positions are not highly paid, but they are paid. Usually they receive 50% of the hourly rate which equates to roughly 20-30k per year.
But to be fair, the only students receiving internships let alone paid ones in this economy are the upper 5-10% of the class. There is no other state or city that has more paid internships, the number available everywhere is extremely low and that fact is very common knowledge among everyone in the industry, in grad school or thinking about grad school. If she was told anything different she was lied to.