When giving a puppy their "booster" shots a week apart, do they still work?

I recently adopted a puppy from a shelter. Her three rounds of puppy shots are included in her adoption price. Last week, I took her to the clinic at the shelter and she got her second round of shots. On Tuesday, I took her to the vet because she had a few minor illnesses when I adopted her so she had to go in for her follow up. The vet tech told me that since she is now 4 months, she will need her rabies shot. Even though this is free at the shelter, I went ahead and told them to give it to her. I informed the vet tech that she had just received her second shots. Next thing I know, the veterinarian comes in and gives two shots very quickly. I asked why she had two and the doctor told me it was rabies and her 2nd boosters. I told the vet that she had the 2nd shot already and the vet told me not to worry about it..that it wouldn't hurt her. However, a friend told me that her vet said that if shots are given again within two weeks, that it basically cancels the shots out and they are ineffective. Does anyone know if this is true?