Could dye in aircon system cause the aircon pump to fail?



I bought my 80 series with leaky air con and i decided it was time to get it
sorted. the pump is not seized and so all i needed to get it going is to
find the leak. took it to a garage to get the aircon serviced nad after a
vacume check (i insisted of dye) they said it was fine.
Worked fine for a bit but 3 days later i went back as all the gas leaked
out. they put the dye in with some gas and told me to come back after the
weekend. that same day i was on the M4 and smelt something burning so i
turned of the aircon (by now all the gas leaked had out). Soon after all my
dials went, including the electric windows and fan. Pulled over opened the
bonnet and found that the air con clutch had melted and the air con pump is
now seized.
Now i could not start it but to cut a very long story short, removed air
con belt and replaced a fuse and i was on my way.
This pump failure seems too much of a coincidence to me. I have been told
that the pump will not engage the clutch if there is no gas so i did not
worry about leaving the air con on. My suspicion is that it has some thing
to do with the dye fooling the pump into thinking there was freon in the
system. What do you guys think? should i pay for a new pump or should the
garage pay for it?
Oh and the dye found a leak in the system, just above the pump...
Rob Wronski