Parts of the story are corroborated in this account (Grado, Gary. "Charges urged in raid in which house burned." East Valley Tribune. Oct 15 2004), which is based on a statement from the sheriff's spokesperson:
Eric Kush, 26, who wasn’t the burglary suspect, refused to come out of the house when SWAT members ordered him to, so they shot tear gas through the windows.
The SWAT team made its way up the stairs of the two story home to look for Kush and sprayed his aggressive pit bull with a fire extinguisher, said Sgt. Paul Chagolla, a sheriff’s spokesman.
Chagolla said the noise of an extinguisher and the plume of fire retardant scares dogs without harming them.
As SWAT members looked for Kush upstairs, they realized the house had caught fire.
The parts of the claim re: deputies laughing, or the dog's remains having been left there, are not mentioned in this article, or any others that I have found.
The sheriff's spokesperson also confirmed that the armored personnel carrier rolled down the street and damaged a car:
The personnel carrier crashed when its engine shut off as a deputy moved it, reducing its braking capacity, Chagolla said.
The vehicle rolled down an incline and came to rest against the car, damaging its hood and front bumper.
An article in the Arizona Republic (Collom, Lindsey. "SWAT Called to Nab Suspect, Ahwatukee Peace Shattered." Arizona Republic. Jul 29 2004) offers a similar account, and corroborates the estimated cost of the damage to the house:
As Kush surrendered, the home burned, the flames consuming a large portion of the roof. [Phoenix Fire Department Capt. Elby] Bushong estimated the damage at $250,000. He said it may be a total loss.
An article in the Arizona Republic (Collom, Lindsey. "County SWAT Action Leads to New Policy." Arizona Republic. Aug 13 2004) also corroborates the part about the police (and neighbors) not having been notified in advance:
When the Maricopa County Sheriff's Office converged on an Ahwatukee Foothills neighborhood last month, residents weren't the only ones surprised.
So were Phoenix police.
The department was not warned about the operation and didn't know what the men in black and green were doing. The Ahwatukee Foothills substation was inundated with calls from concerned residents and the media the morning of July 23 when an armored vehicle and numerous SWAT personnel swarmed Chandler Boulevard and 19th Avenue.
that Kush was wanted on a misdemeanor for failing to appear in traffic court, and that
the SWAT team fired several gas canisters into the house. Fire erupted in the master bedroom on the second level of the home moments later.
Another account can be found here (Murphy, Doug. "Sheriff's SWAT raid opens door to questions." Ahwatukee Foothills News. Aug 04 2004). This article includes a comment from a neighbor:
Neighbor Scott Marlow said that he thought he heard as many as 16 loud bangs as deputies fired tear gas canisters into the 1,375-square-foot home.
and some more statements from those who lived in the house.
Another article (Murphy, Doug. "Sheriff's office seeks charges in house raid." Ahwatukee Foothills News. Oct 20 2004) also suggests that the deputies forced the dog back into the house:
During the raid the home caught fire, deputies forced Kush's dog into the house where it died, and a SWAT armored personnel carrier rolled into a parked car.
and it also cites the same report from the sheriff's office as the Oct. '04 East Valley Tribune article:
The report states that as SWAT members searched the house, a pit bull came toward them. Deputies used a fire extinguisher to scare the dog away and into the master bedroom.
As tear gas was being shot into the house, a fire erupted in the master bedroom. Phoenix fire officials say the $225,000 home and its contents were a total loss.