I experienced exactly what you are experiencing. I noticed blood in my daughter's poop, only hers wasn't a tinge, it was all mixed in with the poop - quite a bit! It was her only problematic symptom - she was gaining weight fine, sleeping fine, not in any apparent pain, hardly was fussy. I was told the same things as you - switch your diet, if that doesn't work, go on formula.
I was NOT okay with switching to formula. Breastmilk is so far above and beyond formula in the benefits it gives your child. Switch to formula, and you're upping your child's chance of dying of SIDS, having diabetes, being overweight, having allergies... DON'T DO IT! Not to mention, breastmilk is always easier on your baby's GI tract than even the most broken-down formulas. Pediatricians do their best, but they are NOT educated in breastfeeding. You might think a week of formula won't hurt, but it destroys the protective lining that breastfeeding creates in your baby.
After my daughter's (who is 4 1/2 months old) pediatrician told me we NEEDED to switch to formula, I went to a second pediatrician to see what he would say. He said if my daughter is gaining well, happy, and doesn't appear to be in pain, there is no rush to put her on formula and we can take plenty of time to try to figure out what is causing it. He said it was causing NO PERMANENT DAMAGE.
That put my mind somewhat at ease, but her first pediatrician still wanted me to switch, so I had her refer me to a GI specialist. We went to see him yesterday. Remember, this is a person who went to school SPECIFICALLY for this type of problem, and he also went to school for pediatrics. He knows what he's talking about. Anyways, he told me that as long as she is gaining well, is happy, isn't in pain, that this isn't hurting her at ALL. He said it is VERY common in infants for them to have blood in their stool, that they outgrow it between 9-12 months.
Now, if your baby is extremely fussy, has a distended stomach, and isn't gaining weight, then I might go along with letting her be scoped. I would NOT, under ANY circumstances, switch her to formula. And, if she is happy, gaining well, not crying in pain, I would NOT do the scoping. It is painful, and has many potential harmful, even fatal side effects.
I know that her doctor is probably making you feel very worried, like this is very serious, but I would seek second and third opinions. Also, email Dr. Jack Newman. If you go to his website, you can email him, and he responds promptly. He is well-known for his expertise in breastfeeding and common problems.
I know what you are going through, and I honestly think pediatricians don't have a clue what they are talking about if they try to tell you formula is better than breastmilk. It isn't. They are misinformed. I also think if the blood is your child's only symptom, it isn't probably a big deal. I'm sensing that you aren't 100% on board with what your pediatrician is telling you. Trust your instincts. Seek as many opinions as necessary until you find one that sounds best for your baby. Hang in there!