Yep I've heard some saying that. Oscar has done his job covering attacking and defensive line and swap position with Fabi to enhance whole team's mobility, ok I get that. But "hardworking" is never a term to justify world class winger/am. Work rate is one of most basic abilities needed in Mourinho's squad, and Ramires, Willian, Mikel all have that.
Since Mourinho only played a 45 minutes attacking football, I will just analyse Oscar's performance during 1st half.
1) He dropped the ball too easily. Whenever he's dribbling, holding, trying to make spaces, he always caught by Burnley players (yes it's only Burnley) and it's always endanger the team when someone lost his ball.
2) As you can see, Oscar had run all along the pitch and he was hardworking. But did you see him making clearance or standing in the right spot when Burnley players were attacking? No, it's always Matic and 4 defenders who do the job.
3) Ok defensive work is not main priority for an am/winger. He should be contributing deadly passes (Fabi's specialty), has great vision on how the team organizing attacking, defensive works on the pitch (Matic, Fabi's specialty), or dribbling, running, and trying to tear out opponent's defence whenever the chances come (Hazard's expertise), this is what attacking players should do. Instead, whenever I saw someone passed the ball to Oscar, he is running backwards and going back to defensive line (what the...?!), he was destroying every attacking chances given to him when the forwards were running and expecting him to do counter attacks or passes a through ball, in another word, he is slowing the team and not the opposite.
In fact, he was almost non-existent when Burnley scored their first goal, and Chelsea made a comeback with 1,2,3 goals thanks to Costa, Fabi, and Schurrle. How was this helping the team? I don't know. When someone is in that position, we should expect him to be contributing to goals and not only give credit for time wasting or mere coordination when team has secured a victory.
Oscar has been given a lot of chances.
Last season, Mou gave him chances and alienate Mata. Mata was transferred out and he went invisible. In the end, Chelsea got nothing.
During World Cup, he was absolute first team and playmaker in Brazil. Brazil won all its matches by small margin only because of Neymar and pure luck. When Neymar was out, you saw what happen to Brazil.
And now, we're talking about the first match. When it comes to "overshadow" , I think it applies to Hazard (failed to gain an assist or goal coz of Fabi's brilliance and Mou's tactic), but certainly it does not apply to Oscar.
Oscar may be good (depend on certain standards) but he is not World Class.
Chelsea is World Class, Mou is World Class, the defending line is ...hence we only lack 1 more am/winger.
Anyway, this is just my sincere opinion and I have no intention to offend anyone.
Feel free to have discussion with me (whether you agree or not) but let's avoid flaming with each other.
ps: Considering the threads above, looks like everyone think Oscar did ok and it seems I'm the Black Sheep here.
Well I certainly hopes that Chelsea continue achieving good result, and ultimately win the League Title (with all the efforts, Mourinho really should) and therefore I wish for the best of Oscar and hope he can assist, score goals and play beautiful football to prove me wrong in the near future.

that is why i think he did ok for the last game. not great. decent game for his standard. not exceptional.
i dont think mikel or ramires suit our passing game (we pass a lot in last match). both mikel and ramires have limited range in their passing, not to mention poor first touch.
agree on oscar performance after mata departure. i am one of the guy from 'mata team' and keep on dwelling on 'if only we have mata, we could have win the game' last season. not once, not twice, but almost everytime when the team fail to perform.
hazard done pretty well imo. successfully dribble past numbers of defender, click well with our attacking dept, tracking back & cover for dave. same old hazrd.
for world cup performance, everyone from our contingent play poorly bar schurrle.
current squad good enough for me. got top class cover for each position. our 'second' team can challenge for top4 spot imo.
p/s: i think our defence quite shaky in the last game. cahill and terry both have their share of sloppy moment.