Miami Beach cops claim Justin Bieber was drag racing at the time of his arrest Thursday ... but the facts seem to show the allegation is MADE UP ... because we've learned they were actually UNDER THE SPEED LIMIT in the middle of the so-called drag race.

According to the police report ... cops spotted Justin and his buddy Khalil drag racing at around 4 AM.

The police report says ... an officer observed the 2 vehicles reaching speeds between 55 and 60 MPH.

Now the problems.  

Cops say they noticed the "drag race" on the 2600 block of Pine Tree Drive.  Cops were traveling in the opposite direction so they made a U turn and pursued the cars for 15 blocks.

Mind you ... Justin was driving one of the fastest race cars around -- a Lamborghini Gallardo LP550-2 Spyder.  Khalil was driving a Ferrari 16M.  Cops claim 2 SUVs in Justin's entourage actually blocked off traffic to give the 2 a clear path.  

So how could a 15-block drag race in those cars reach speeds of ONLY 60 MPH?

Fact is ... THEY DIDN'T EVEN REACH 60.  IN FACT THEY DIDN'T EVEN REACH 50.  THEY DIDN'T EVEN 
REACH 40.

TMZ has learned ... the place where Justin and Khalil rented the cars attached a GPS device that also tracks speed.  

The GPS clocked both cars at 27 MPH at the 3500 block of Pine Tree Drive ... smack in the middle of the so-called "drag race."

There's only one time they ever broke 50 MPH and that was long before the pursuit started.  When Justin and Khalil left the club, one car was briefly clocked at 52 MPH and the other 47 MPH. Both drivers slowed down pretty quick and 5 blocks before cops noticed them they were going 34 MPH in a 30 MPH zone.   Blocks later, they were steady at 27 MPH.

 So it seems cops goosed the facts to justify the stop.

And that's not the only problem with the police report.  TMZ broke the story ... Justin's blood alcohol level was .014 -- a barely measurable amount.  Yet cops claim Justin reeked of alcohol both at the scene and at the police department.