Oh yes it does! How well you play includes how well you manage your time. Time is as much part of Chess as it is in other games. In football you could score the greatest goal in history, but if the referee blows time before it goes in it doesn't count. Similarly in Chess if you don't get your moves in within the time, you lose, and correctly so.
I could be wrong, but I assume she's talking about blitz games. There are lots of people who are great blitz players but terrible in long games, and vice versa.
I agree with you fischer, she is talking about blitz (/ live chess).
According to me,what Becca wanted to say is "our rating does not state how good or bad we play but it depends on our playing rate( It is just a yard stick). WE NEED TO LOOK AT IT(rating) IN ORDER TO IMPROVE US and rather it should not discourage us."
If you check out the Glicko formula you'll realise this is caused by different RDs (rating deviations). To put it in simple terms, a player who plays often has a more accurate rating than someone who plays occassionaly. They therefore have a lower RD and their rating will change less after each game, because it's considered to be fairly accurate.
Because your opponent's rating was considered more accurate (he had a lower RD), it changed less than yours.