You are wrong. :)
One thing to remember here is that as with any other hosting provider, "GoDaddy" can mean many things.
Shared hosting, Virtual Private Hosting (VPS), Dedicated Server hosting, and lastly the network uptime, which is separate from how the servers behave.
If your competitor has setup their hosting on a cheap shared-hosting server, then yes, they might have some trouble, simply because of the number of other domains they will be sharing Web- and database servers with.
If you check the IPs of some hosting companies shared hosts, you can easily find that a single IP carry up to maybe 4000+ "web-sites" on it. Even though maybe 90% of these "sites" are mere junk or parked domains with no traffic, they still represent competition for the server's attention. Typically slow, in other words, and almost surely not able to handle high traffic spikes, such as on a successful advertising campaign. If that business requires running scripts on the server for data-processing or loading, there will also be failures because of memory limitations.
If your competitor has their site hosted on a VPS (a server time-sliced into looking like multiple individual servers), they might be sharing with potentially 50-100 other domains/customers. It all depends. Again, it will take away some of their ability to handle spikes. Plus it limits the amount of memory they can "own". Typically to maybe 512Mb or less.
If your competitor leased a dedicated server from GoDaddy (or anywhere else), they would have the whole server's attention to themselves, and it would serve only their domain(s). No different from if they owned and located the server at their business location directly, or if they used a co-location site. You are then down to the only difference being how well the network performs. The server behind that competitor would be the same as anywhere else, and depends only in how much money they put into configuring that server (how many GB of RAM and how many CPU cores mostly).
The Godaddy networks as such has in my experience had superb support. In all my years there I have never experienced any real network downtime. A side-effect of Godaddy's data-centers servicing thousands of large and small sites 24x7, having alternate routes, ... . I personally pump many GBs of data through those networks, both in outgoing traffic from sites and from data pushed into my servers through large data uploads 24x7 every day.
If you look at dedicated server level service, the only real difference between Godaddy type hosting and such as RackSpace and others is one of flexibility. At hosters such as Godaddy, you configure a standardized type configuration. Define what you need in memory, disk, and so on from a standardized list.
For example a Linux server, 8GB RAM, 600 GB disk, Plesk control panel, ... They build one, stick the OS on it, and put it in your account. Takes no time at all.
At some other hosters, you can do that plus you can choose to have very personalized server setups for specialized needs (at a much higher price of course). For example define and acquire your own large RAID units, extra large memory setups, and much such. That goes more in the direction of co-location type setups, where you own everything yourself, but locate it in someone else's datacenter.
Once upon a time many years ago, I had a site running on a shared server setup. Not really a good experience.
Everything since then have been dedicated Linux servers in max configurations (I am an old Unix/Linux geek), and I have never had an issue. I manage my own stuff and my own configurations, and they keep my servers, firewall units, and network powered up and communicating.
Bottom-line. You wont know about your competitor, unless you know exactly what they purchased from Godaddy (or anywhere else they might go).
When many people think of Godaddy, they think "Walmart of cheap domains", "bad advertising for the masses on the Superbowl", or maybe even "unprofessional".. But that is merely because most people think in terms of the shared hosting setups, and the advertising they see for the masses, and associate that branding as "GoDaddy". But there is more to it.
Also, as far a competition goes, do not discount the fact that your competitor might be able to buy twice the dedicated server power you pay for elsewhere. Upping their site speed, which leads to increased Google priority, cheaper ads on Adwords, ... :)
Just saying.. :)