> I've read that due to the constant leaking while on the tarmac they would have to immediately rendezvous with a tanker to refuel after takeoff.

To reduce structural loads the aircraft took off with a very light fuel load and refuelled in flight.

Rather interestingly, the modern fascination with SR-71 stories and facts has turned a rather mundane "weeping" of fuel into the much more exciting image of fuel almost gushing out of cracks in the fuselage at such a rate it had to be refuelled immediately after takeoff!