Let's derive the running time of the median of medians algorithm. Since you can use Google, you already know that the answer is O(n). But do you know why?
Median of medians is a divide-and-conquer algorithm. In each stage of the recursion, we split the array into K subarrays and recurse on them. To combine the results of those recursions, we do a constant amount of work.
So the running time for an array of length N is
T(n) = kT(n/k) + C
where k and C are constants. Usually K=5.
Luckily, we can solve this recurrence with case one of the master theorem. This gives a running time of O(n).
What if, instead, we did O(n) work to combine the results of the recursions? This is essentially what you are claiming.
Then the recurrence would be
T(n) = kT(n/k) + Cn + D
where k, C, and D are constants.
By case 2 of the master theorem, the running time would be O(n log n).
Incidentally, this is the reason why quicksort's running time is O(n log n)-- because it does O(n) work before doing each recursion. In quicksort's case, k = 2.
Anyone can use Google and find the running time of an algorithm. But unless you can derive it, you do not truly understand it. Perhaps you need to do a little bit less talking and a little bit more listening.