They'd likely lose the "independent contractor" argument if drivers weren't able to work for both companies simultaneously. It's hard to say someone is an "employee" if they're logged into competitors' apps and taking rides from either, during the same shift.

I agree with your reasoning, but I think that's not really necessary to ride both Lyft and Uber to justify "independent contractor" status. The fact that Lyft riders use their own cars and choose their own working hours (i.e no direct supervision from Lyft side) should be enough to justify that.