Oh, come on! Those were actually some of the few times picking on Beauregard was funny! Probably because it was the guest star in the first one.
Here's another Vet's Hospital where, surprise surprise, they DID NOT pick on Beau:
(Dr. Bob comes up with a miners hat and pick)
"Dr. Bob! You can't use a pick on the patient!"
- Nurse Piggy
"I can on the patients pocket! Now, where is he?"
- Dr. Bob
"Right here, Dr. Bob. He was trying to fix the lights when he got a severe shock!"
- Nurse Janice
"When he sees who his Doctor is, he'll get another one."
- Piggy
"Noooo, not that! He's had ten-thousand volts!"
- Janice
"Oh, good! That should be enough to get him elected!"
- Dr. Bob
"Noooooooo, not Votes! Volts!"
- Janice
"Oh, well then, run some volts through him again!"
- Dr. Bob
"Again???????"
- Piggy & Janice
"Yes! It's called 'Re-volting!'"
- Dr. Bob
"It certainly is!"
- Piggy and Janice
"And now, we come to the end of another Veterinarian's Hospital. Tune in next week when you'll hear Dr. Bob say..."
- Announcer
"If the light's still out when the patient comes to, give him this."
- Dr. Bob
"What? That's a ball-point pen with a little light on it!"
- Piggy
"Yes! it's so he can see to sign a check!"
- Dr. Bob
See, they didn't pick on him. Mainly because he was asleep.