I’ve been reviewing some of my sequences lately, and found one that I took with my mobile phone (Nexus 4) mounted on my bike. I made my own mount, which is pretty firm, but the phone’s camera is simply sub-par.
Consider this sequence: http://www.mapillary.com/map/im/-fNORLq3YUAHpVwP2BQHIQ/photo If you advance a few photos, you can also see how poorly it adjusts to light. That’s going up a mountain at about 7mph (11km/h). If you turn around on that same road, you can see how shaky it gets at about 30mph (48km/h) (e.g http://www.mapillary.com/map/im/DvUD6XgTNtQEeAFBQnGy1A/photo).
In comparison, the sequence you linked is superb. I’d say disable the shake check and see how the photos look, and if they’re not great, put it back on. Alternatively, as Anders said, an action camera might be a good option. I just bought three of these, which were on sale for about $50 USD with shipping. Example: http://www.mapillary.com/map/im/PE5iNuiiujsV3iY0Z1JmuA/photo