Please give her the benefit of the doubt. She said, "I trim his nails," not "I trimmed his nails." It's not the best verb conjugation, but it could be referring to the fact that she is the person who regularly trims his nails, or that she will trim his nails in the future. Either way, it's not important, and calling the OP a liar is not helpful.
Now that that is out of the way, even if it is a nosebleed, a nosebleed can be a sign of an underlying disorder that needs to be diagnosed and treated:
Nose Bleed in Dogs | petMD Epitaxis (Nose Bleed) in Dogs and Cats | MyPetED
The photo doesn't look like the dog was peeing blood. If it was pee in the blood, it would be diluted and not as bright. I've never heard of a dog peeing pure blood, but I suppose anything is possible.
Whether it's a nose bleed or peeing blood, please see the vet. I don't think your vets are lazy (at least, not the second vet), but they DO want to be paid for their services. If you think either of these vets is not competent to diagnose your dog, find another vet, but please see a vet and take the pee pad with you.