The claim's numbers of 600, 140, and 20 need to be put in context. The 600-count was on a "particularly dirty tablet", not the typical tablet. They go on to say the "typical toilet seat we tested had a Staphylococcus count of less than 20 units". That greatly weakens the claim, but the general message it conveys is supported by other studies.
In (Scott 2008), they found that 14% of toilet seats, 15% of kitchen phones, and 13% of phones in general tested positive for S aureus.
In (Scott 2009), they counted occurrences of "coagulase-negative (CN) Staphylococcus sp, methicillin-sensitive Staphyloccus aureus (MSSA) and MRSA, Pseudomonas sp, and members of the Enterobacteriaceae." The 25th percentile, median, and 75th percentile counts for the surfaces in question were found to be:
- Toilet bowl: 0, 0, 4.7×106
- Toilet seat: 0, 0, 80
- Kitchen phone: 0, 40, 450
Those two studies don't directly address the exact claim in question. They compared toilet seats to fixed household and office phones, not mobile phones. (Scott 2008) only looked at percentage of surfaces that were contaminated, not bacterial counts, and (Scott 2009) reported bacterial counts, but not isolated to Staphylococcus aureus. However, the claim in the question is not contradicted by these studies' findings. For example, the kitchen phones were found to have a higher bacterial count (across all species of interest) than the toilet seat.
(Walia 2014) gives an explanation: "they come into contact with more parts of our body and a wider range of bacteria than toilet seats", and "this type of bacteria multiply at high temperatures and our phones are perfect for breeding these germs, as they’re kept warm and cozy in our pockets, handbags and brief cases".
The bacterial contamination of mobile phones is a recognized risk in the clinical setting. (Visvanathan 2012) says, "It is concerning that these devices have been found to harbor such a variety of multidrug-resistant pathogens", and "Mobile phone decontamination to reduce the risk of cross contamination has been widely advocated." Only 50.9% of patients "had ever cleaned their phones".
What should you do about this? Just use an alcohol wipe. "Decolonization with 70% isopropyl alcohol is simple, cheap, and induces a proven significant reduction of bioburden in most reported studies" (Visvanathan 2012).
Scott, E., Duty, S., & Callahan, M. (2008). A pilot study to isolate Staphylococcus aureus and methicillin-resistant S aureus from environmental surfaces in the home. American journal of infection control, 36(6), 458-460.
Scott, E., Duty, S., & McCue, K. (2009). A critical evaluation of methicillin-resistant Staphylococcus aureus and other bacteria of medical interest on commonly touched household surfaces in relation to household demographics. American journal of infection control, 37(6), 447-453.
Visvanathan, A., Rodrigues, M. A., Brady, R., & Gibb, A. P. (2012). Mobile phone usage in the clinical setting: Evidence-based guidelines for all users is urgently required. American journal of infection control, 40(1), 86-87.
Walia, S. S., Manchanda, A., & Narang, R. S. (2014). Cellular telephone as reservoir of bacterial contamination: myth or fact. Journal of clinical and diagnostic research: JCDR, 8(1), 50.