I'm very fortunate in this respect. I ride 50k/year and a lot of that is due to work (and of course I go through the mountains, et el as much as possible).
I have broken down a few times. It costs me out of pocket, I do not infringe upon my employer whatsoever regarding time used to ride and/or other issues. I do not charge for motels I use if my route takes any longer than a flight.
In turn, they leave me alone for the most part. There was some concern after my oct crash but I still managed to work 4 hrs/day from home during the first month or so.
It simply amazes me that TRANSPORTATION you use can be dictated by an employer unless you are a salesman or something, regarding the perception issue.
Honestly, if that was a policy I had to live with, well, I wouldn't. Unless you are making millions (NFL, etc) or something (who knows where the cut line should be, if at all), it just ain't right.
oh, by the way, before my first ever crash/total with 265k on bikes, my worst injuries ever were on a mountain bike, which I rode to work every day for 5 years (except winter), 25 miles/day. No one ever said anything about that, even though I hit or got hit by cars at least 2x per commuting season (was in MI at the time). And I had 15k miles on just one of my bicycles. Now you know why I switched to motorbikes again!